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Welcome to Chemistry

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12-5: Reaction Mechanism

12-5-1: Learning Objectives

Learning Objectives

One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system, such as the rate of change in the concentration of reactants or products with time, to discover the sequence of events that occur at the molecular level during a reaction. This molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products. The stepwise changes are collectively called the reaction mechanism.

In an internal combustion engine, for example, isooctane reacts with oxygen to give carbon dioxide and water:

2C8H18(l)+25O2( g)⟶16CO2( g)+18H2O(g)2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{l})+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})

For this reaction to occur in a single step, 25 dioxygen molecules and 2 isooctane molecules would have to collide simultaneously and be converted to 34 molecules of product, which is very unlikely. It is more likely that a complex series of reactions takes place in a stepwise fashion. Each individual reaction, which is called an elementary reaction, involves one, two, or (rarely) three atoms, molecules, or ions. The overall sequence of elementary reactions is the mechanism of the reaction. The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.

The overall sequence of elementary reactions is the mechanism of the reaction.

12-5-2: Molecularity and the Rate-Determining Step

To demonstrate how the analysis of elementary reactions helps us determine the overall reaction mechanism, we will examine the much simpler reaction of carbon monoxide with nitrogen dioxide.

2CO+2NO2→2CO2+N2O4\mathrm{2CO + 2NO_2 \rightarrow 2CO_2 + N_2O_4}

From the balanced chemical equation, one might expect the reaction to occur via a collision of one molecule of NO2\mathrm{NO}_{2} with a molecule of CO\mathrm{CO} that results in the transfer of an oxygen atom from nitrogen to carbon. The experimentally determined rate law for the reaction, however, is as follows:

 rate =k[NO2]2\text { rate }=k\left[\mathrm{NO}_{2}\right]^{2}

The fact that the reaction is second order in [NO2]\left[\mathrm{NO}_{2}\right] and independent of [CO][\mathrm{CO}] tells us that it does not occur by the simple collision model outlined previously. If it did, its predicted rate law would be

 rate =k[NO2][CO].\text { rate }=k\left[\mathrm{NO}_{2}\right][\mathrm{CO}] .

The following two-step mechanism is consistent with the rate law if step 1 is much slower than step 2:

15-2-1: Two-Step Mechanism

StepsReactionReaction Type
step 1NO2+NO2⟶ slow NO3+NO\mathrm{NO}_{2}+\mathrm{NO}_{2} \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}_{3}+\mathrm{NO}elementary reaction
step 2NO3+CO→NO2+CO2‾\underline{\mathrm{NO}_{3}+\mathrm{CO} \rightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}}elementary reaction
sumNO2+CO→NO+CO2\mathrm{NO}_{2}+\mathrm{CO} \rightarrow \mathrm{NO}+\mathrm{CO}_{2}overall reaction

According to this mechanism, the overall reaction occurs in two steps, or elementary reactions. Summing steps 1 and 2 and canceling on both sides of the equation gives the overall balanced chemical equation for the reaction. The NO3\mathrm{NO_3} molecule is intermediate in the reaction, a species that does not appear in the balanced chemical equation for the overall reaction. It is formed as a product of the first step but is consumed in the second step.

The sum of the elementary reactions in a reaction mechanism must give the overall balanced chemical equation of the reaction.

12-5-3: Using Molecularity to Describe a Rate Law

The molecularity of an elementary reaction is the number of molecules that collide during that step in the mechanism. If there is only a single reactant molecule in an elementary reaction, that step is designated as unimolecular; if there are two reactant molecules, it is bimolecular; and if there are three reactant molecules (a relatively rare situation), it is termolecular. Elementary reactions that involve the simultaneous collision of more than three molecules are highly improbable and have never been observed experimentally. (To understand why, try to make three or more marbles or pool balls collide with one another simultaneously!)

About the image

The Basis for Writing Rate Laws of Elementary Reactions. This diagram illustrates how the number of possible collisions per unit time between two reactant species, A and B, depends on the number of A and B particles present. The number of collisions between A and B particles increases as the product of the number of particles, not as the sum. This is why the rate law for an elementary reaction depends on the product of the concentrations of the species that collide in that step. (CC BY-NC-SA; anonymous)

Writing the rate law for an elementary reaction is straightforward because we know how many molecules must collide simultaneously for the elementary reaction to occur; hence the order of the elementary reaction is the same as its molecularity (Table 14.6.1). In contrast, the rate law for the reaction cannot be determined from the balanced chemical equation for the overall reaction. The general rate law for a unimolecular elementary reaction ( A→\mathrm{A} \rightarrow products) is

 rate =k[A].\text { rate }=k[A] .

For bimolecular reactions, the reaction rate depends on the number of collisions per unit time, which is proportional to the product of the concentrations of the reactants, as shown in Figure 14.6.1 For a bimolecular elementary reaction of the form A+B→\mathrm{A}+\mathrm{B} \rightarrow products, the general rate law is

 rate =k[A][B].\text { rate }=k[A][B] .

Elementary ReactionMolecularityRateReaction Order
A→ products \mathrm{A} \rightarrow \text { products }Unimolecular rate =k[ A]\text { rate }=k[\mathrm{~A}]first
2 A→ products 2\mathrm{~A} \rightarrow \text { products }Bimolecular rate =k[ A]2\text { rate }=k[\mathrm{~A}]^2second
A+B→ products \mathrm{A}+\mathrm{B} \rightarrow \text { products }Bimolecular rate =k[ A][B]\text { rate }=k[\mathrm{~A}][\mathrm{B}]second
2 A+B→ products 2 \mathrm{~A}+\mathrm{B} \rightarrow \text { products }Termolecular rate =k[ A]2[ B]\text { rate }=k[\mathrm{~A}]^2[\mathrm{~B}]third
A+B+C→ products \mathrm{A}+\mathrm{B}+\mathrm{C} \rightarrow \text { products }Termolecular rate =k[ A][B][C]\text { rate }=k[\mathrm{~A}][\mathrm{B}][\mathrm{C}]third

For elementary reactions, the order of the elementary reaction is the same as its molecularity. In contrast, the rate law cannot be determined from the balanced chemical equation for the overall reaction (unless it is a single step mechanism and is therefore also an elementary step).

12-5-4: Identifying the Rate-Determining Step

Note the important difference between writing rate laws for elementary reactions and the balanced chemical equation of the overall reaction. Because the balanced chemical equation does not necessarily reveal the individual elementary reactions by which the reaction occurs, we cannot obtain the rate law for a reaction from the overall balanced chemical equation alone. In fact, it is the rate law for the slowest overall reaction, which is the same as the rate law for the slowest step in the reaction mechanism, the ratedetermining step, that must give the experimentally determined rate law for the overall reaction.This statement is true if one step is substantially slower than all the others, typically by a factor of 10 or more. If two or more slow steps have comparable rates, the experimentally determined rate laws can become complex. Our discussion is limited to reactions in which one step can be identified as being substantially slower than any other. The reason for this is that any process that occurs through a sequence of steps can take place no faster than the slowest step in the sequence. In an automotive assembly line, for example, a component cannot be used faster than it is produced. Similarly, blood pressure is regulated by the flow of blood through the smallest passages, the capillaries. Because movement through capillaries constitutes the rate-determining step in blood flow, blood pressure can be regulated by medications that cause the capillaries to contract or dilate. A chemical reaction that occurs via a series of elementary reactions can take place no faster than the slowest step in the series of reactions.

Look at the rate laws for each elementary reaction in the example as well as for the overall reaction.

Rate laws for each elementary reaction in our example as well as for the overall reaction

StepsReactionRate
step 1NO2+NO2→k1NO3+NO\mathrm{NO}_2+\mathrm{NO}_2 \stackrel{\mathrm{k}_1}{\rightarrow} \mathrm{NO}_3+\mathrm{NO} rate =k1[NO2]2( predicted) \text { rate }=k_1\left[\mathrm{NO}_2\right]^2(\text { predicted) }
step 2NO3+CO→k2NO2+CO2‾\underline{\mathrm{NO}_3+\mathrm{CO} \stackrel{k_2}{\rightarrow} \mathrm{NO}_2+\mathrm{CO}_2} rate =k2[NO3][CO]( predicted )\text { rate }=k_2\left[\mathrm{NO}_3\right][\mathrm{CO}](\text { predicted })
step 3NO2+CO→kNO+CO2\mathrm{NO}_2+\mathrm{CO} \stackrel{k}{\rightarrow} \mathrm{NO}+\mathrm{CO}_2 rate =k[NO2]2( observed) \text { rate }=k\left[\mathrm{NO}_2\right]^2(\text { observed) }

The experimentally determined rate law for the reaction of NO2\mathrm{NO}_{2} with COC O is the same as the predicted rate law for step 1 . This tells us that the first elementary reaction is the rate-determining step, so kk for the overall reaction must equal k1k_{1}. That is, NO3\mathrm{NO}_{3} is formed slowly in step 1, but once it is formed, it reacts very rapidly with CO in step 2.

Sometimes chemists are able to propose two or more mechanisms that are consistent with the available data. If a proposed mechanism predicts the wrong experimental rate law, however, the mechanism must be incorrect.

12-5-4-1: Example-A Reaction with an Intermediate

In an alternative mechanism for the reaction of NO2\mathrm{NO}_{2} with CO\mathrm{CO} with N2O4\mathrm{N}_{2} \mathrm{O}_{4} appearing as an intermediate.

alternative mechanism for the reaction of NO2\mathrm{NO}_{2} with CO\mathrm{CO} with N2O4\mathrm{N}_{2} \mathrm{O}_{4} appearing as an intermediate.

Write the rate law for each elementary reaction. Is this mechanism consistent with the experimentally determined rate law (rate =k[NO2]2t=\mathrm{k[{NO}_{2}]^{2}t})

Given: elementary reactions Asked for: rate law for each elementary reaction and overall rate law

Strategy

  • Determine the rate law for each elementary reaction in the reaction.

  • Determine which rate law corresponds to the experimentally determined rate law for the reaction. This rate law is the one for the rate-determining step.

Solution

View solution

A The rate law for step 1 is rate =k1[NO2]2=k_{1}\left[\mathrm{NO}_{2}\right]^{2}; for step 2 , it is rate =k2[ N2O4][CO]=k_{2}\left[\mathrm{~N}_{2} \mathrm{O}_{4}\right][\mathrm{CO}].

B If step 1 is slow (and therefore the rate-determining step), then the overall rate law for the reaction will be the same: rate == k1[NO2]2k_{1}\left[\mathrm{NO}_{2}\right]^{2}. This is the same as the experimentally determined rate law. Hence this mechanism, with N2O4\mathrm{N}_{2} \mathrm{O}_{4} as an intermediate, and the one described previously, with NO3\mathrm{NO}_{3} as an intermediate, are kinetically indistinguishable. In this case, further experiments are needed to distinguish between them. For example, the researcher could try to detect the proposed intermediates, NO3\mathrm{NO}_{3} and N2O4\mathrm{N}_{2} \mathrm{O}_{4}, directly.

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12-5: Reaction Mechanism

12-5-1: Learning Objectives

Learning Objectives

One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system, such as the rate of change in the concentration of reactants or products with time, to discover the sequence of events that occur at the molecular level during a reaction. This molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products. The stepwise changes are collectively called the reaction mechanism.

In an internal combustion engine, for example, isooctane reacts with oxygen to give carbon dioxide and water:

2C8H18(l)+25O2( g)⟶16CO2( g)+18H2O(g)2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{l})+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})

For this reaction to occur in a single step, 25 dioxygen molecules and 2 isooctane molecules would have to collide simultaneously and be converted to 34 molecules of product, which is very unlikely. It is more likely that a complex series of reactions takes place in a stepwise fashion. Each individual reaction, which is called an elementary reaction, involves one, two, or (rarely) three atoms, molecules, or ions. The overall sequence of elementary reactions is the mechanism of the reaction. The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.

The overall sequence of elementary reactions is the mechanism of the reaction.

12-5-2: Molecularity and the Rate-Determining Step

To demonstrate how the analysis of elementary reactions helps us determine the overall reaction mechanism, we will examine the much simpler reaction of carbon monoxide with nitrogen dioxide.

2CO+2NO2→2CO2+N2O4\mathrm{2CO + 2NO_2 \rightarrow 2CO_2 + N_2O_4}

From the balanced chemical equation, one might expect the reaction to occur via a collision of one molecule of NO2\mathrm{NO}_{2} with a molecule of CO\mathrm{CO} that results in the transfer of an oxygen atom from nitrogen to carbon. The experimentally determined rate law for the reaction, however, is as follows:

 rate =k[NO2]2\text { rate }=k\left[\mathrm{NO}_{2}\right]^{2}

The fact that the reaction is second order in [NO2]\left[\mathrm{NO}_{2}\right] and independent of [CO][\mathrm{CO}] tells us that it does not occur by the simple collision model outlined previously. If it did, its predicted rate law would be

 rate =k[NO2][CO].\text { rate }=k\left[\mathrm{NO}_{2}\right][\mathrm{CO}] .

The following two-step mechanism is consistent with the rate law if step 1 is much slower than step 2:

15-2-1: Two-Step Mechanism

StepsReactionReaction Type
step 1NO2+NO2⟶ slow NO3+NO\mathrm{NO}_{2}+\mathrm{NO}_{2} \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}_{3}+\mathrm{NO}elementary reaction
step 2NO3+CO→NO2+CO2‾\underline{\mathrm{NO}_{3}+\mathrm{CO} \rightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}}elementary reaction
sumNO2+CO→NO+CO2\mathrm{NO}_{2}+\mathrm{CO} \rightarrow \mathrm{NO}+\mathrm{CO}_{2}overall reaction

According to this mechanism, the overall reaction occurs in two steps, or elementary reactions. Summing steps 1 and 2 and canceling on both sides of the equation gives the overall balanced chemical equation for the reaction. The NO3\mathrm{NO_3} molecule is intermediate in the reaction, a species that does not appear in the balanced chemical equation for the overall reaction. It is formed as a product of the first step but is consumed in the second step.

The sum of the elementary reactions in a reaction mechanism must give the overall balanced chemical equation of the reaction.

12-5-3: Using Molecularity to Describe a Rate Law

The molecularity of an elementary reaction is the number of molecules that collide during that step in the mechanism. If there is only a single reactant molecule in an elementary reaction, that step is designated as unimolecular; if there are two reactant molecules, it is bimolecular; and if there are three reactant molecules (a relatively rare situation), it is termolecular. Elementary reactions that involve the simultaneous collision of more than three molecules are highly improbable and have never been observed experimentally. (To understand why, try to make three or more marbles or pool balls collide with one another simultaneously!)

About the image

The Basis for Writing Rate Laws of Elementary Reactions. This diagram illustrates how the number of possible collisions per unit time between two reactant species, A and B, depends on the number of A and B particles present. The number of collisions between A and B particles increases as the product of the number of particles, not as the sum. This is why the rate law for an elementary reaction depends on the product of the concentrations of the species that collide in that step. (CC BY-NC-SA; anonymous)

Writing the rate law for an elementary reaction is straightforward because we know how many molecules must collide simultaneously for the elementary reaction to occur; hence the order of the elementary reaction is the same as its molecularity (Table 14.6.1). In contrast, the rate law for the reaction cannot be determined from the balanced chemical equation for the overall reaction. The general rate law for a unimolecular elementary reaction ( A→\mathrm{A} \rightarrow products) is

 rate =k[A].\text { rate }=k[A] .

For bimolecular reactions, the reaction rate depends on the number of collisions per unit time, which is proportional to the product of the concentrations of the reactants, as shown in Figure 14.6.1 For a bimolecular elementary reaction of the form A+B→\mathrm{A}+\mathrm{B} \rightarrow products, the general rate law is

 rate =k[A][B].\text { rate }=k[A][B] .

Elementary ReactionMolecularityRateReaction Order
A→ products \mathrm{A} \rightarrow \text { products }Unimolecular rate =k[ A]\text { rate }=k[\mathrm{~A}]first
2 A→ products 2\mathrm{~A} \rightarrow \text { products }Bimolecular rate =k[ A]2\text { rate }=k[\mathrm{~A}]^2second
A+B→ products \mathrm{A}+\mathrm{B} \rightarrow \text { products }Bimolecular rate =k[ A][B]\text { rate }=k[\mathrm{~A}][\mathrm{B}]second
2 A+B→ products 2 \mathrm{~A}+\mathrm{B} \rightarrow \text { products }Termolecular rate =k[ A]2[ B]\text { rate }=k[\mathrm{~A}]^2[\mathrm{~B}]third
A+B+C→ products \mathrm{A}+\mathrm{B}+\mathrm{C} \rightarrow \text { products }Termolecular rate =k[ A][B][C]\text { rate }=k[\mathrm{~A}][\mathrm{B}][\mathrm{C}]third

For elementary reactions, the order of the elementary reaction is the same as its molecularity. In contrast, the rate law cannot be determined from the balanced chemical equation for the overall reaction (unless it is a single step mechanism and is therefore also an elementary step).

12-5-4: Identifying the Rate-Determining Step

Note the important difference between writing rate laws for elementary reactions and the balanced chemical equation of the overall reaction. Because the balanced chemical equation does not necessarily reveal the individual elementary reactions by which the reaction occurs, we cannot obtain the rate law for a reaction from the overall balanced chemical equation alone. In fact, it is the rate law for the slowest overall reaction, which is the same as the rate law for the slowest step in the reaction mechanism, the ratedetermining step, that must give the experimentally determined rate law for the overall reaction.This statement is true if one step is substantially slower than all the others, typically by a factor of 10 or more. If two or more slow steps have comparable rates, the experimentally determined rate laws can become complex. Our discussion is limited to reactions in which one step can be identified as being substantially slower than any other. The reason for this is that any process that occurs through a sequence of steps can take place no faster than the slowest step in the sequence. In an automotive assembly line, for example, a component cannot be used faster than it is produced. Similarly, blood pressure is regulated by the flow of blood through the smallest passages, the capillaries. Because movement through capillaries constitutes the rate-determining step in blood flow, blood pressure can be regulated by medications that cause the capillaries to contract or dilate. A chemical reaction that occurs via a series of elementary reactions can take place no faster than the slowest step in the series of reactions.

Look at the rate laws for each elementary reaction in the example as well as for the overall reaction.

Rate laws for each elementary reaction in our example as well as for the overall reaction

StepsReactionRate
step 1NO2+NO2→k1NO3+NO\mathrm{NO}_2+\mathrm{NO}_2 \stackrel{\mathrm{k}_1}{\rightarrow} \mathrm{NO}_3+\mathrm{NO} rate =k1[NO2]2( predicted) \text { rate }=k_1\left[\mathrm{NO}_2\right]^2(\text { predicted) }
step 2NO3+CO→k2NO2+CO2‾\underline{\mathrm{NO}_3+\mathrm{CO} \stackrel{k_2}{\rightarrow} \mathrm{NO}_2+\mathrm{CO}_2} rate =k2[NO3][CO]( predicted )\text { rate }=k_2\left[\mathrm{NO}_3\right][\mathrm{CO}](\text { predicted })
step 3NO2+CO→kNO+CO2\mathrm{NO}_2+\mathrm{CO} \stackrel{k}{\rightarrow} \mathrm{NO}+\mathrm{CO}_2 rate =k[NO2]2( observed) \text { rate }=k\left[\mathrm{NO}_2\right]^2(\text { observed) }

The experimentally determined rate law for the reaction of NO2\mathrm{NO}_{2} with COC O is the same as the predicted rate law for step 1 . This tells us that the first elementary reaction is the rate-determining step, so kk for the overall reaction must equal k1k_{1}. That is, NO3\mathrm{NO}_{3} is formed slowly in step 1, but once it is formed, it reacts very rapidly with CO in step 2.

Sometimes chemists are able to propose two or more mechanisms that are consistent with the available data. If a proposed mechanism predicts the wrong experimental rate law, however, the mechanism must be incorrect.

12-5-4-1: Example-A Reaction with an Intermediate

In an alternative mechanism for the reaction of NO2\mathrm{NO}_{2} with CO\mathrm{CO} with N2O4\mathrm{N}_{2} \mathrm{O}_{4} appearing as an intermediate.

alternative mechanism for the reaction of NO2\mathrm{NO}_{2} with CO\mathrm{CO} with N2O4\mathrm{N}_{2} \mathrm{O}_{4} appearing as an intermediate.

Write the rate law for each elementary reaction. Is this mechanism consistent with the experimentally determined rate law (rate =k[NO2]2t=\mathrm{k[{NO}_{2}]^{2}t})

Given: elementary reactions Asked for: rate law for each elementary reaction and overall rate law

Strategy

  • Determine the rate law for each elementary reaction in the reaction.

  • Determine which rate law corresponds to the experimentally determined rate law for the reaction. This rate law is the one for the rate-determining step.

Solution

View solution

A The rate law for step 1 is rate =k1[NO2]2=k_{1}\left[\mathrm{NO}_{2}\right]^{2}; for step 2 , it is rate =k2[ N2O4][CO]=k_{2}\left[\mathrm{~N}_{2} \mathrm{O}_{4}\right][\mathrm{CO}].

B If step 1 is slow (and therefore the rate-determining step), then the overall rate law for the reaction will be the same: rate == k1[NO2]2k_{1}\left[\mathrm{NO}_{2}\right]^{2}. This is the same as the experimentally determined rate law. Hence this mechanism, with N2O4\mathrm{N}_{2} \mathrm{O}_{4} as an intermediate, and the one described previously, with NO3\mathrm{NO}_{3} as an intermediate, are kinetically indistinguishable. In this case, further experiments are needed to distinguish between them. For example, the researcher could try to detect the proposed intermediates, NO3\mathrm{NO}_{3} and N2O4\mathrm{N}_{2} \mathrm{O}_{4}, directly.

+ diff --git a/academic/chemistry/problems/02-20.html b/academic/chemistry/problems/02-20.html index 6cd06ba5..327f39d2 100644 --- a/academic/chemistry/problems/02-20.html +++ b/academic/chemistry/problems/02-20.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Presentation problem: 02-20

Question

At 500 K500 \mathrm{~K} in the presence of a copper surface, ethanol decomposes according to the equation

C2H5OH(g)⟶CH3CHO(g)+H2(g)\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(\mathrm{g}) \longrightarrow \mathrm{CH}_3 \mathrm{CHO}(g)+\mathrm{H}_2(g)

The pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} was measured as a function of time and the following data were obtained:

Time (s)PC2H5OH (torr) P_{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}} \text { (torr) }
0250.
100.237
200.224
300.211
400.198
500.185

Since the pressure of a gas is directly proportional to the concentration of gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the above data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} after 900.s900 . \mathrm{s} from the start of the reaction. (Hint: To determine the order of the reaction with respect to C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}, compare how the pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} decreases with each time listing.)

Solution

solution graph

Due to the fact that the graph of p[O2]\mathrm{p}\left[\mathrm{O}_2\right] over time is showing R2\mathrm{R}^2 value of 1 we know we have a zero-order reaction. Therefore:

k=p0[C2H5OH]−p[C2H5OH]t=250 torr −185 torr 500 s=0.13 torr s −1k=0.13 torr s s−1×1 atm760 torr =1.71×10−4 atm s−1 rate =kp(C2H5OH)=−kt+p0(C2H5OH)p(C2H5OH)=−(1.71×10−4 atm s−1)×900 s+0.33 atmp(C2H5OH)=0.176 atm s−1\begin{aligned} & \mathrm{k}=\frac{\mathrm{p}_0\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]-\mathrm{p}\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]}{\mathrm{t}}=\frac{250 \text { torr }-185 \text { torr }}{500 \mathrm{~s}}=0.13 \text { torr s }^{-1} \\ & \mathrm{k}=0.13 \text { torr s } \mathrm{s}^{-1} \times \frac{1 \mathrm{~atm}}{760 \text { torr }}=1.71 \times 10^{-4} \mathrm{~atm} \mathrm{~s}^{-1} \\ & \text { rate }=\mathbf{k} \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=-\mathrm{kt}+\mathrm{p}_0\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right) \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=-\left(1.71 \times 10^{-4} \mathrm{~atm} \mathrm{~s}^{-1}\right) \times 900 \mathrm{~s}+0.33 \mathrm{~atm} \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=0.176 \mathrm{~atm} \mathrm{~s}^{-1} \\ & \end{aligned}

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Presentation problem: 02-20

Question

At 500 K500 \mathrm{~K} in the presence of a copper surface, ethanol decomposes according to the equation

C2H5OH(g)⟶CH3CHO(g)+H2(g)\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(\mathrm{g}) \longrightarrow \mathrm{CH}_3 \mathrm{CHO}(g)+\mathrm{H}_2(g)

The pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} was measured as a function of time and the following data were obtained:

Time (s)PC2H5OH (torr) P_{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}} \text { (torr) }
0250.
100.237
200.224
300.211
400.198
500.185

Since the pressure of a gas is directly proportional to the concentration of gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the above data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} after 900.s900 . \mathrm{s} from the start of the reaction. (Hint: To determine the order of the reaction with respect to C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}, compare how the pressure of C2H5OH\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} decreases with each time listing.)

Solution

solution graph

Due to the fact that the graph of p[O2]\mathrm{p}\left[\mathrm{O}_2\right] over time is showing R2\mathrm{R}^2 value of 1 we know we have a zero-order reaction. Therefore:

k=p0[C2H5OH]−p[C2H5OH]t=250 torr −185 torr 500 s=0.13 torr s −1k=0.13 torr s s−1×1 atm760 torr =1.71×10−4 atm s−1 rate =kp(C2H5OH)=−kt+p0(C2H5OH)p(C2H5OH)=−(1.71×10−4 atm s−1)×900 s+0.33 atmp(C2H5OH)=0.176 atm s−1\begin{aligned} & \mathrm{k}=\frac{\mathrm{p}_0\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]-\mathrm{p}\left[\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right]}{\mathrm{t}}=\frac{250 \text { torr }-185 \text { torr }}{500 \mathrm{~s}}=0.13 \text { torr s }^{-1} \\ & \mathrm{k}=0.13 \text { torr s } \mathrm{s}^{-1} \times \frac{1 \mathrm{~atm}}{760 \text { torr }}=1.71 \times 10^{-4} \mathrm{~atm} \mathrm{~s}^{-1} \\ & \text { rate }=\mathbf{k} \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=-\mathrm{kt}+\mathrm{p}_0\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right) \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=-\left(1.71 \times 10^{-4} \mathrm{~atm} \mathrm{~s}^{-1}\right) \times 900 \mathrm{~s}+0.33 \mathrm{~atm} \\ & \mathrm{p}\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)=0.176 \mathrm{~atm} \mathrm{~s}^{-1} \\ & \end{aligned}

+ diff --git a/academic/chemistry/problems/03-02-1.html b/academic/chemistry/problems/03-02-1.html index 9b59bea2..afc06094 100644 --- a/academic/chemistry/problems/03-02-1.html +++ b/academic/chemistry/problems/03-02-1.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Problem: 03-02-1

Question

2 N2O5(g)→4NO2(g)+O2(g)2 \mathrm{~N}_2 \mathrm{O}_5(g) \rightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)

The decomposition of N2O5(g)\mathrm{N}_2 \mathrm{O}_5(g) is represented by the equation above. A sample of N2O5(g)\mathrm{N}_2 \mathrm{O}_5(g) is monitored as it decomposes, and the concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 as a function of time is recorded. The results are shown in the table below.

Time (s)[N2O5]\mathrm{[N_2O_5]}
01.000
25.00.801
50.00.642
75.00.515

Calculate the average rate of the reaction between 50.050.0 and 75.075.0 seconds.

Solution

a A+b B→cC+dDa \mathrm{~A}+b \mathrm{~B} \rightarrow c \mathrm{C}+d \mathrm{D}

the rate of reaction is defined as

 rate =−1aΔ[A]Δt=−1bΔ[B]Δt=+1cΔ[C]Δt=+1dΔ[D]Δt\color{cyan}\text { rate }=-\frac{1}{a} \frac{\Delta[\mathrm{A}]}{\Delta t}=-\frac{1}{b} \frac{\Delta[\mathrm{B}]}{\Delta t}=+\frac{1}{c} \frac{\Delta[\mathrm{C}]}{\Delta t}=+\frac{1}{d} \frac{\Delta[\mathrm{D}]}{\Delta t}

Notice that the rate of change in concentration of each species is divided by its coefficient from the balanced chemical equation ( aa, b,cb, c, or dd ). This ensures that the calculated reaction rate is the same no matter which reactant or product is monitored for changes in concentration. In this case, the monitored species was N2O5\mathrm{N}_2 \mathrm{O}_5. With that in mind, let's write the reaction rate in terms of the rate of change in concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 :

 rate =−12Δ[N2O5]Δt\text { rate }=-\frac{1}{2} \frac{\Delta\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\Delta t}

Since the coefficient for N2O5\mathrm{N}_2 \mathrm{O}_5 in the balanced equation is 2 , we divided the rate of change in concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 by 2 . Additionally, since N2O5\mathrm{N}_2 \mathrm{O}_5 is being consumed in the reaction, we included a negative sign in front of the expression.

Now, let's plug in the information from the table to calculate the average reaction rate between 50.050.0 and 75.075.0 seconds:

 rate =−12(0.515M−0.642M)(75.0 s−50.0 s)=2.54×10−3M s−1\begin{aligned} \text { rate } & =-\frac{1}{2} \frac{(0.515 M-0.642 M)}{(75.0 \mathrm{~s}-50.0 \mathrm{~s})} \\ & =2.54 \times 10^{-3} M \mathrm{~s}^{-1} \end{aligned}

So, the average rate of the reaction between 50.050.0 and 75.075.0 seconds is 2.54×10−3Ms−1\bold{2.54 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1}}.

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Problem: 03-02-1

Question

2 N2O5(g)→4NO2(g)+O2(g)2 \mathrm{~N}_2 \mathrm{O}_5(g) \rightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)

The decomposition of N2O5(g)\mathrm{N}_2 \mathrm{O}_5(g) is represented by the equation above. A sample of N2O5(g)\mathrm{N}_2 \mathrm{O}_5(g) is monitored as it decomposes, and the concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 as a function of time is recorded. The results are shown in the table below.

Time (s)[N2O5]\mathrm{[N_2O_5]}
01.000
25.00.801
50.00.642
75.00.515

Calculate the average rate of the reaction between 50.050.0 and 75.075.0 seconds.

Solution

a A+b B→cC+dDa \mathrm{~A}+b \mathrm{~B} \rightarrow c \mathrm{C}+d \mathrm{D}

the rate of reaction is defined as

 rate =−1aΔ[A]Δt=−1bΔ[B]Δt=+1cΔ[C]Δt=+1dΔ[D]Δt\color{cyan}\text { rate }=-\frac{1}{a} \frac{\Delta[\mathrm{A}]}{\Delta t}=-\frac{1}{b} \frac{\Delta[\mathrm{B}]}{\Delta t}=+\frac{1}{c} \frac{\Delta[\mathrm{C}]}{\Delta t}=+\frac{1}{d} \frac{\Delta[\mathrm{D}]}{\Delta t}

Notice that the rate of change in concentration of each species is divided by its coefficient from the balanced chemical equation ( aa, b,cb, c, or dd ). This ensures that the calculated reaction rate is the same no matter which reactant or product is monitored for changes in concentration. In this case, the monitored species was N2O5\mathrm{N}_2 \mathrm{O}_5. With that in mind, let's write the reaction rate in terms of the rate of change in concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 :

 rate =−12Δ[N2O5]Δt\text { rate }=-\frac{1}{2} \frac{\Delta\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\Delta t}

Since the coefficient for N2O5\mathrm{N}_2 \mathrm{O}_5 in the balanced equation is 2 , we divided the rate of change in concentration of N2O5\mathrm{N}_2 \mathrm{O}_5 by 2 . Additionally, since N2O5\mathrm{N}_2 \mathrm{O}_5 is being consumed in the reaction, we included a negative sign in front of the expression.

Now, let's plug in the information from the table to calculate the average reaction rate between 50.050.0 and 75.075.0 seconds:

 rate =−12(0.515M−0.642M)(75.0 s−50.0 s)=2.54×10−3M s−1\begin{aligned} \text { rate } & =-\frac{1}{2} \frac{(0.515 M-0.642 M)}{(75.0 \mathrm{~s}-50.0 \mathrm{~s})} \\ & =2.54 \times 10^{-3} M \mathrm{~s}^{-1} \end{aligned}

So, the average rate of the reaction between 50.050.0 and 75.075.0 seconds is 2.54×10−3Ms−1\bold{2.54 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1}}.

+ diff --git a/academic/chemistry/problems/03-02-2.html b/academic/chemistry/problems/03-02-2.html index cf0b03aa..c6bc6c9e 100644 --- a/academic/chemistry/problems/03-02-2.html +++ b/academic/chemistry/problems/03-02-2.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Problem: 03-02-2

Question

The rate law for a particular reaction is rate =k[XY]2=k[\mathrm{XY}]^2. In an experiment, the initial rate of the reaction is determined to be 0.16 mol/(L⋅s)0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) when the initial concentration of XY\mathrm{XY} is 0.40 mol/L0.40 \mathrm{~mol} / \mathrm{L}.

  • What is the value of the rate constant, kk, for the reaction?
    • 0.10 L/(mol⋅s)0.10 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 0.40 L/(mol⋅s)0.40 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 1.0 L/(mol⋅s)1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 2.5 L/(mol⋅s)2.5 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})

Solution

lo tind the value of the rate constant for the reaction, let's first solve the rate law for kk :

k= rate [XY]2k=\frac{\text { rate }}{[\mathrm{XY}]^2}

Next, let's plug in the initial rate and concentration given in the text:

k=0.16 mol/(L⋅s)(0.40 mol/L)2=0.16 mol/(L⋅s)0.16 mol2/L2=1.0 L/(mol⋅s)\begin{aligned} k & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{(0.40 \mathrm{~mol} / \mathrm{L})^2} \\ & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{0.16 \mathrm{~mol}^2 / \mathrm{L}^2} \\ & =1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) \end{aligned}

So, the value of the rate constant for the reaction is 1.0 L/(mol⋅s)1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})

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Problem: 03-02-2

Question

The rate law for a particular reaction is rate =k[XY]2=k[\mathrm{XY}]^2. In an experiment, the initial rate of the reaction is determined to be 0.16 mol/(L⋅s)0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) when the initial concentration of XY\mathrm{XY} is 0.40 mol/L0.40 \mathrm{~mol} / \mathrm{L}.

  • What is the value of the rate constant, kk, for the reaction?
    • 0.10 L/(mol⋅s)0.10 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 0.40 L/(mol⋅s)0.40 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 1.0 L/(mol⋅s)1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 2.5 L/(mol⋅s)2.5 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})

Solution

lo tind the value of the rate constant for the reaction, let's first solve the rate law for kk :

k= rate [XY]2k=\frac{\text { rate }}{[\mathrm{XY}]^2}

Next, let's plug in the initial rate and concentration given in the text:

k=0.16 mol/(L⋅s)(0.40 mol/L)2=0.16 mol/(L⋅s)0.16 mol2/L2=1.0 L/(mol⋅s)\begin{aligned} k & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{(0.40 \mathrm{~mol} / \mathrm{L})^2} \\ & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{0.16 \mathrm{~mol}^2 / \mathrm{L}^2} \\ & =1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s}) \end{aligned}

So, the value of the rate constant for the reaction is 1.0 L/(mol⋅s)1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})

+ diff --git a/academic/chemistry/problems/03-02-3.html b/academic/chemistry/problems/03-02-3.html index a163b89a..ebd03b16 100644 --- a/academic/chemistry/problems/03-02-3.html +++ b/academic/chemistry/problems/03-02-3.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Problem 03-02-3

Question

2X(g)+2Y(g)→Q(g)+2R(g)2 \mathrm{X}(g)+2 \mathrm{Y}(g) \rightarrow \mathrm{Q}(g)+2 \mathrm{R}(g)

The reaction represented above is found to be second order with respect to X\mathrm{X} and first order with respect to Y\mathrm{Y}.

What happens to the rate of the reaction when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled?

  • It increases by a factor of 4.
  • It decreases by a factor of 2.
  • It decreases by a factor of 4.
  • It does not change.

Solution

To solve this problem, let's first write out the rate law for the reaction. According to the text, the reaction is second order with respect to X\mathrm{X} and first order with respect to Y\mathrm{Y}, so the rate law is rate =k[X]2[Y]=k[\mathrm{X}]^2[\mathrm{Y}]

Now, let's think about how the rate changes when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled. Since [X][\mathrm{X}] is raised to the second power in the rate law, halving [X][\mathrm{X}] decreases the reaction rate by a factor of 4 . Similarly, since [Y][\mathrm{Y}] is raised to the first power, doubling [Y][\mathrm{Y}] increases the reaction rate by a factor of 2 . Combined, these changes result in the reaction rate decreasing by a factor of 2 overall. So, when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled, the rate of the reaction decreases by a factor of 2 .

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Problem 03-02-3

Question

2X(g)+2Y(g)→Q(g)+2R(g)2 \mathrm{X}(g)+2 \mathrm{Y}(g) \rightarrow \mathrm{Q}(g)+2 \mathrm{R}(g)

The reaction represented above is found to be second order with respect to X\mathrm{X} and first order with respect to Y\mathrm{Y}.

What happens to the rate of the reaction when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled?

  • It increases by a factor of 4.
  • It decreases by a factor of 2.
  • It decreases by a factor of 4.
  • It does not change.

Solution

To solve this problem, let's first write out the rate law for the reaction. According to the text, the reaction is second order with respect to X\mathrm{X} and first order with respect to Y\mathrm{Y}, so the rate law is rate =k[X]2[Y]=k[\mathrm{X}]^2[\mathrm{Y}]

Now, let's think about how the rate changes when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled. Since [X][\mathrm{X}] is raised to the second power in the rate law, halving [X][\mathrm{X}] decreases the reaction rate by a factor of 4 . Similarly, since [Y][\mathrm{Y}] is raised to the first power, doubling [Y][\mathrm{Y}] increases the reaction rate by a factor of 2 . Combined, these changes result in the reaction rate decreasing by a factor of 2 overall. So, when [X][\mathrm{X}] is halved and [Y][\mathrm{Y}] is doubled, the rate of the reaction decreases by a factor of 2 .

+ diff --git a/academic/literature/index.html b/academic/literature/index.html index 152ab0ba..94f804ec 100644 --- a/academic/literature/index.html +++ b/academic/literature/index.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Welcome to Literature

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Welcome to Literature

+ diff --git a/academic/literature/writing/methods-of-development.html b/academic/literature/writing/methods-of-development.html index c698fe34..b761e606 100644 --- a/academic/literature/writing/methods-of-development.html +++ b/academic/literature/writing/methods-of-development.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Patterns of Organization and Methods of Development

Patterns of organization can help your readers follow the ideas within your essay and your paragraphs, but they can also work as methods of development to help you recognize and further develop ideas and relationships in your writing. Here are some strategies that can help you with both organization and development in your essays.

Major Patterns of Organization

A fruit pie.

Read the following sentences:

  • Now take the pie out of the oven and let it cool on the stovetop.
  • Mix the dry ingredients with the liquid ingredients.
  • Set the pie crust aside while you make the filling.

How did it feel to read the above list? A bit confusing, I would guess. That’s because the steps for making a pie were not well organized, and the steps don’t include enough detail for us to know exactly what we should do. (Like what are the dry and liquid ingredients?) We all know that starting instructions from the beginning and giving each detailed step in the order it should happen is vital to having a good outcome, in this case a yummy pie! But it’s not always so simple to know how to organize or develop ideas, and sometimes there’s more than one way, which complicates things even further.

First, let’s take a look at a couple of ways to think about organization.

General to Specific or Specific to General

It might be useful to think about organizing your topic like a triangle:

Two triangles. The first is an inverted pyramid for General to Specific, the second is a pyramid for Specific to General.

The first triangle represents starting with the most general, big picture information first, moving then to more detailed and often more personal information later in the paper. The second triangle represents an organizational structure that starts with the specific, small scale information first and then moves to the more global, big picture stuff.

For example, if your topic is traffic in Vancouver, British Columbia, an essay that uses the general-to-specific organizational structure might begin this way:

Many people consider Vancouver, British Columbia, to be a relaxed place to live. They would be shocked to know how bad the traffic is traveling major arteries into the city and even driving around the city itself.

An essay that uses the specific-to-general structure might start like this:

Transit is crowded, parking is expensive, and vehicles stop and go through the main streets of the city of Vancouver, British Columbia, and that is just once travelers brave the crowded arteries to enter the city; Vancouver’s traffic problem does not lend itself to the relaxed atmosphere many believe the city to have.

What’s the difference between these two introductions? And how might they appeal to the intended audience for this essay in different ways? The first introduction is looking at the big picture of the problem and mentions pollution’s impact on all citizens in Portland, while the second introduction focuses on one specific family. The first helps readers see how vast the problem really is, and the second helps connect readers to a real family, making an emotional appeal from the very beginning. Neither introduction is necessarily better. You’ll choose one over the other based on the kind of tone you’d like to create and how you’d like to affect your audience. It’s completely up to you to make this decision.

Does the Triangle Mean the Essay Keeps Getting More Specific or More Broad until the Very End?

The triangle is kind of a general guide, meaning you’re allowed to move around within it all you want. For example, it’s possible that each of your paragraphs will be its own triangle, starting with the general or specific and moving out or in. However, if you begin very broadly, it might be effective to end your essay in a more specific, personal way. And if you begin with a personal story, consider ending your essay by touching on the global impact and importance of your topic.

Are There Other Ways to Think about Organizing My Ideas?

Yes! Rather than thinking about which of your ideas are most specific or personal or which are more broad or universal, you might consider one of the following ways of organizing your ideas:

  • Most important information first (consider what you want readers to focus on first)
  • Chronological order (the order in time that events take place)
  • Compare and contrast (ideas are organized together because of their relationship to each other)

The section on Methods of Development, below, offers more detail about some of these organizational patterns, along with some others.

Choose one of the following topics, and practice writing a few opening sentences like we did above, once using the general-to-specific format and once using the specific-to-general. Which do you like better? What audience would be attracted to which one? Share with peers to see how others tackled this challenge. How would you rewrite their sentences? Why? Discuss your changes and listen to how your peers have revised your sentences. Taking in other people’s ideas will help you see new ways to approach your own writing and thinking.
Topics:

  • Facing fears
  • Safety in sports
  • Community policing
  • Educating prisoners
  • Sex education

Methods of Development

The methods of development covered here are best used as ways to look at what’s already happening in your draft and to consider how you might emphasize or expand on any existing patterns. You might already be familiar with some of these patterns because teachers will sometimes assign them as the purpose for writing an essay. For example, you might have been asked to write a cause-and-effect essay or a comparison-and-contrast essay.

It’s important to emphasize here that patterns of organization or methods of developing content usually happen naturally as a consequence of the way the writer engages with and organizes information while writing. That is to say, most writers don’t sit down and say, “I think I’ll write a cause-and-effect essay today.” Instead, a writer might be more likely to be interested in a topic, say, the state of drinking water in the local community, and as the writer begins to explore the topic, certain cause-and-effect relationships between environmental pollutants and the community water supply may begin to emerge.

So if these patterns just occur naturally in writing, what’s the use in knowing about them? Well, sometimes you might be revising a draft and notice that some of your paragraphs are a bit underdeveloped. Maybe they lack a clear topic, or maybe they lack support. In either case, you can look to these common methods of development to find ways to sharpen those vague topics or to add support where needed. Do you have a clear cause statement somewhere but you haven’t explored the effects? Are you lacking detail somewhere where a narrative story or historical chronology can help build reader interest and add support? Are you struggling to define an idea that might benefit from some comparison or contrast? Read on to consider some of the ways that these strategies can help you in revision.

Cause and Effect (or Effect and Cause)

Do you see a potential cause-and-effect relationship developing in your draft? The cause-and-effect pattern may be used to identify one or more causes followed by one or more effects or results. Or you may reverse this sequence and describe effects first and then the cause or causes. For example, the causes of water pollution might be followed by its effects on both humans and animals. You may use obvious transitions to clarify cause and effect, such as “What are the results? Here are some of them…” or you might simply use the words cause, effect, and result, to cue the reader about your about the relationships that you’re establishing.

Problem-Solution

At some point does your essay explore a problem or suggest a solution? The problem-solution pattern is commonly used in identifying something that’s wrong and in contemplating what might be done to remedy the situation. There are probably more ways to organize a problem-solution approach, but but here are three possibilities:

  • Describe the problem, followed by the solution.
  • Propose the solution first and then describe the problems that motivated it.
  • Or a problem may be followed by several solutions, one of which is selected as the best.

When the solution is stated at the end of the paper, the pattern is sometimes called the delayed proposal. For a hostile audience, it may be effective to describe the problem, show why other solutions do not work, and finally suggest the favored solution. You can emphasize the words problem and solution to signal these sections of your paper for your reader.

Chronology or Narrative

Do you need to develop support for a topic where telling a story can illustrate some important concept for your readers? Material arranged chronologically is explained as it occurs in time. A chronological or narrative method of development might help you find a way to add both interest and content to your essay. Material arranged chronologically is explained as it occurs in time. This pattern may be used to establish what has happened. Chronology or narrative can be a great way to introduce your essay by providing a background or history behind your topic. Or you may want to tell a story to develop one or more points in the body of your essay. You can use transitional words like then, next, and finally to make the parts of the chronology clear.

Comparison and Contrast

Are you trying to define something? Do you need your readers to understand what something is and what it is not? The comparison-and-contrast method of development is particularly useful in extending a definition, or anywhere you need to show how a subject is like or unlike another subject. For example, the statement is often made that drug abuse is a medical problem instead of a criminal justice issue. An author might attempt to prove this point by comparing drug addiction to AIDS, cancer, or heart disease to redefine the term “addiction” as a medical problem. A statement in opposition to this idea could just as easily establish contrast by explaining all the ways that addiction is different from what we traditionally understand as an illness. In seeking to establish comparison or contrast in your writing, some words or terms that might be useful are by contrast, in comparison, while, some, and others.

Summary

These four methods of development—cause and effect, problem-solution, chronology or narrative, and comparison and contrast—are just a few ways to organize and develop ideas and content in your essays. It’s important to note that they should not be a starting point for writers who want to write something authentic—something that they care deeply about. Instead, they can be a great way to help you look for what’s already happening with your topic or in a draft, to help you to write more, or to help you reorganize some parts of an essay that seem to lack connection or feel disjointed. Look for organizational patterns when you’re reading work by professional writers. Notice where they combine strategies (e.g., a problem-solution pattern that uses cause-and-effect organization, or a comparison-contrast pattern that uses narrative or chronology to develop similarities or differences). Pay attention to how different writers emphasize and develop their main ideas, and use what you find to inspire you in your own writing. Better yet, work on developing completely new patterns of your own.

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Patterns of Organization and Methods of Development

Patterns of organization can help your readers follow the ideas within your essay and your paragraphs, but they can also work as methods of development to help you recognize and further develop ideas and relationships in your writing. Here are some strategies that can help you with both organization and development in your essays.

Major Patterns of Organization

A fruit pie.

Read the following sentences:

  • Now take the pie out of the oven and let it cool on the stovetop.
  • Mix the dry ingredients with the liquid ingredients.
  • Set the pie crust aside while you make the filling.

How did it feel to read the above list? A bit confusing, I would guess. That’s because the steps for making a pie were not well organized, and the steps don’t include enough detail for us to know exactly what we should do. (Like what are the dry and liquid ingredients?) We all know that starting instructions from the beginning and giving each detailed step in the order it should happen is vital to having a good outcome, in this case a yummy pie! But it’s not always so simple to know how to organize or develop ideas, and sometimes there’s more than one way, which complicates things even further.

First, let’s take a look at a couple of ways to think about organization.

General to Specific or Specific to General

It might be useful to think about organizing your topic like a triangle:

Two triangles. The first is an inverted pyramid for General to Specific, the second is a pyramid for Specific to General.

The first triangle represents starting with the most general, big picture information first, moving then to more detailed and often more personal information later in the paper. The second triangle represents an organizational structure that starts with the specific, small scale information first and then moves to the more global, big picture stuff.

For example, if your topic is traffic in Vancouver, British Columbia, an essay that uses the general-to-specific organizational structure might begin this way:

Many people consider Vancouver, British Columbia, to be a relaxed place to live. They would be shocked to know how bad the traffic is traveling major arteries into the city and even driving around the city itself.

An essay that uses the specific-to-general structure might start like this:

Transit is crowded, parking is expensive, and vehicles stop and go through the main streets of the city of Vancouver, British Columbia, and that is just once travelers brave the crowded arteries to enter the city; Vancouver’s traffic problem does not lend itself to the relaxed atmosphere many believe the city to have.

What’s the difference between these two introductions? And how might they appeal to the intended audience for this essay in different ways? The first introduction is looking at the big picture of the problem and mentions pollution’s impact on all citizens in Portland, while the second introduction focuses on one specific family. The first helps readers see how vast the problem really is, and the second helps connect readers to a real family, making an emotional appeal from the very beginning. Neither introduction is necessarily better. You’ll choose one over the other based on the kind of tone you’d like to create and how you’d like to affect your audience. It’s completely up to you to make this decision.

Does the Triangle Mean the Essay Keeps Getting More Specific or More Broad until the Very End?

The triangle is kind of a general guide, meaning you’re allowed to move around within it all you want. For example, it’s possible that each of your paragraphs will be its own triangle, starting with the general or specific and moving out or in. However, if you begin very broadly, it might be effective to end your essay in a more specific, personal way. And if you begin with a personal story, consider ending your essay by touching on the global impact and importance of your topic.

Are There Other Ways to Think about Organizing My Ideas?

Yes! Rather than thinking about which of your ideas are most specific or personal or which are more broad or universal, you might consider one of the following ways of organizing your ideas:

  • Most important information first (consider what you want readers to focus on first)
  • Chronological order (the order in time that events take place)
  • Compare and contrast (ideas are organized together because of their relationship to each other)

The section on Methods of Development, below, offers more detail about some of these organizational patterns, along with some others.

Choose one of the following topics, and practice writing a few opening sentences like we did above, once using the general-to-specific format and once using the specific-to-general. Which do you like better? What audience would be attracted to which one? Share with peers to see how others tackled this challenge. How would you rewrite their sentences? Why? Discuss your changes and listen to how your peers have revised your sentences. Taking in other people’s ideas will help you see new ways to approach your own writing and thinking.
Topics:

  • Facing fears
  • Safety in sports
  • Community policing
  • Educating prisoners
  • Sex education

Methods of Development

The methods of development covered here are best used as ways to look at what’s already happening in your draft and to consider how you might emphasize or expand on any existing patterns. You might already be familiar with some of these patterns because teachers will sometimes assign them as the purpose for writing an essay. For example, you might have been asked to write a cause-and-effect essay or a comparison-and-contrast essay.

It’s important to emphasize here that patterns of organization or methods of developing content usually happen naturally as a consequence of the way the writer engages with and organizes information while writing. That is to say, most writers don’t sit down and say, “I think I’ll write a cause-and-effect essay today.” Instead, a writer might be more likely to be interested in a topic, say, the state of drinking water in the local community, and as the writer begins to explore the topic, certain cause-and-effect relationships between environmental pollutants and the community water supply may begin to emerge.

So if these patterns just occur naturally in writing, what’s the use in knowing about them? Well, sometimes you might be revising a draft and notice that some of your paragraphs are a bit underdeveloped. Maybe they lack a clear topic, or maybe they lack support. In either case, you can look to these common methods of development to find ways to sharpen those vague topics or to add support where needed. Do you have a clear cause statement somewhere but you haven’t explored the effects? Are you lacking detail somewhere where a narrative story or historical chronology can help build reader interest and add support? Are you struggling to define an idea that might benefit from some comparison or contrast? Read on to consider some of the ways that these strategies can help you in revision.

Cause and Effect (or Effect and Cause)

Do you see a potential cause-and-effect relationship developing in your draft? The cause-and-effect pattern may be used to identify one or more causes followed by one or more effects or results. Or you may reverse this sequence and describe effects first and then the cause or causes. For example, the causes of water pollution might be followed by its effects on both humans and animals. You may use obvious transitions to clarify cause and effect, such as “What are the results? Here are some of them…” or you might simply use the words cause, effect, and result, to cue the reader about your about the relationships that you’re establishing.

Problem-Solution

At some point does your essay explore a problem or suggest a solution? The problem-solution pattern is commonly used in identifying something that’s wrong and in contemplating what might be done to remedy the situation. There are probably more ways to organize a problem-solution approach, but but here are three possibilities:

  • Describe the problem, followed by the solution.
  • Propose the solution first and then describe the problems that motivated it.
  • Or a problem may be followed by several solutions, one of which is selected as the best.

When the solution is stated at the end of the paper, the pattern is sometimes called the delayed proposal. For a hostile audience, it may be effective to describe the problem, show why other solutions do not work, and finally suggest the favored solution. You can emphasize the words problem and solution to signal these sections of your paper for your reader.

Chronology or Narrative

Do you need to develop support for a topic where telling a story can illustrate some important concept for your readers? Material arranged chronologically is explained as it occurs in time. A chronological or narrative method of development might help you find a way to add both interest and content to your essay. Material arranged chronologically is explained as it occurs in time. This pattern may be used to establish what has happened. Chronology or narrative can be a great way to introduce your essay by providing a background or history behind your topic. Or you may want to tell a story to develop one or more points in the body of your essay. You can use transitional words like then, next, and finally to make the parts of the chronology clear.

Comparison and Contrast

Are you trying to define something? Do you need your readers to understand what something is and what it is not? The comparison-and-contrast method of development is particularly useful in extending a definition, or anywhere you need to show how a subject is like or unlike another subject. For example, the statement is often made that drug abuse is a medical problem instead of a criminal justice issue. An author might attempt to prove this point by comparing drug addiction to AIDS, cancer, or heart disease to redefine the term “addiction” as a medical problem. A statement in opposition to this idea could just as easily establish contrast by explaining all the ways that addiction is different from what we traditionally understand as an illness. In seeking to establish comparison or contrast in your writing, some words or terms that might be useful are by contrast, in comparison, while, some, and others.

Summary

These four methods of development—cause and effect, problem-solution, chronology or narrative, and comparison and contrast—are just a few ways to organize and develop ideas and content in your essays. It’s important to note that they should not be a starting point for writers who want to write something authentic—something that they care deeply about. Instead, they can be a great way to help you look for what’s already happening with your topic or in a draft, to help you to write more, or to help you reorganize some parts of an essay that seem to lack connection or feel disjointed. Look for organizational patterns when you’re reading work by professional writers. Notice where they combine strategies (e.g., a problem-solution pattern that uses cause-and-effect organization, or a comparison-contrast pattern that uses narrative or chronology to develop similarities or differences). Pay attention to how different writers emphasize and develop their main ideas, and use what you find to inspire you in your own writing. Better yet, work on developing completely new patterns of your own.

Reference

+ diff --git a/academic/physics/index.html b/academic/physics/index.html index 9acee093..ababd8fb 100644 --- a/academic/physics/index.html +++ b/academic/physics/index.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Welcome to Physics

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Welcome to Physics

+ diff --git a/academic/physics/ipho-formulas-jpn/1.html b/academic/physics/ipho-formulas-jpn/1.html index 9316549d..93b12ce0 100644 --- a/academic/physics/ipho-formulas-jpn/1.html +++ b/academic/physics/ipho-formulas-jpn/1.html @@ -8,7 +8,7 @@ - + @@ -50,8 +50,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​​

1.13: 積分

  1. 積分：微分の公式の左辺と右辺を入れ替えたものと同 じ（逆演算）.例えば,

    ∫xn dx=xn+1/(n+1).\int x^n \mathrm{~d} x=x^{n+1} /(n+1) .

    置換積分の特別な場合 :

    ∫f(ax+b)dx=F(ax+b)/a.\int f(a x+b) \mathrm{d} x=F(a x+b) / a .

1.14: 円錐曲線

  1. 円錐曲線: a11x2+2a12xy+a22y2+a1x+a2y+a0=a_{11} x^2+2 a_{12} x y+a_{22} y^2+a_1 x+a_2 y+a_0= 0 で, a11=a22a_{11}=a_{22} ならば円, a11(a11a22−a122)>0a_{11}\left(a_{11} a_{22}-a_{12}^2\right)>0 ならば楕円, ⋯<0\cdots<0 ならば双曲線, a11a22−a122=0a_{11} a_{22}-a_{12}^2=0 ならば放物線. 楕円 : l1+l2=2a,α1=α2l_1+l_2=2 a, \alpha_1=\alpha_2 [訳 者注 : 焦点と曲線上の点を結ぶ直線と接線とのなす角 ], A=πabA=\pi a b. 双曲線 : l1−l2=2a,α1+α2=0l_1-l_2=2 a, \alpha_1+\alpha_2=0. 放物線 :l+h=: l+h= const., α1=α2\alpha_1=\alpha_2.

1.15: 数值計算 & 台形規則

  1. 数值計算. f(x)=0f(x)=0 の解を求めるニュートン法 :

    xn+1=xn−f(xn)/f′(xn)x_{n+1}=x_n-f\left(x_n\right) / f^{\prime}\left(x_n\right)

    近似積分の台形規則：

    ∫abf(x)dx≈b−a2n[f(x0)+2{f(x1)+⋯ +f(xn−1)}+f(xn)]\begin{array}{r} \int_a^b f(x) \mathrm{d} x \approx \frac{b-a}{2 n}\left[f\left(x_0\right)+2\left\{f\left(x_1\right)+\cdots\right.\right. \left.\left.+f\left(x_{n-1}\right)\right\}+f\left(x_n\right)\right] \end{array}

1.16: ベクトルの微分 & 積分

  1. ベクトルの微分と積分：成分ごとに微分/積分する．あるいは無限に近い22つのベクトルの差を求めることで 微分す.
- +M1001 80h400000v40h-400000z">​​

1.13: 積分

  1. 積分：微分の公式の左辺と右辺を入れ替えたものと同 じ（逆演算）.例えば,

    ∫xn dx=xn+1/(n+1).\int x^n \mathrm{~d} x=x^{n+1} /(n+1) .

    置換積分の特別な場合 :

    ∫f(ax+b)dx=F(ax+b)/a.\int f(a x+b) \mathrm{d} x=F(a x+b) / a .

1.14: 円錐曲線

  1. 円錐曲線: a11x2+2a12xy+a22y2+a1x+a2y+a0=a_{11} x^2+2 a_{12} x y+a_{22} y^2+a_1 x+a_2 y+a_0= 0 で, a11=a22a_{11}=a_{22} ならば円, a11(a11a22−a122)>0a_{11}\left(a_{11} a_{22}-a_{12}^2\right)>0 ならば楕円, ⋯<0\cdots<0 ならば双曲線, a11a22−a122=0a_{11} a_{22}-a_{12}^2=0 ならば放物線. 楕円 : l1+l2=2a,α1=α2l_1+l_2=2 a, \alpha_1=\alpha_2 [訳 者注 : 焦点と曲線上の点を結ぶ直線と接線とのなす角 ], A=πabA=\pi a b. 双曲線 : l1−l2=2a,α1+α2=0l_1-l_2=2 a, \alpha_1+\alpha_2=0. 放物線 :l+h=: l+h= const., α1=α2\alpha_1=\alpha_2.

1.15: 数值計算 & 台形規則

  1. 数值計算. f(x)=0f(x)=0 の解を求めるニュートン法 :

    xn+1=xn−f(xn)/f′(xn)x_{n+1}=x_n-f\left(x_n\right) / f^{\prime}\left(x_n\right)

    近似積分の台形規則：

    ∫abf(x)dx≈b−a2n[f(x0)+2{f(x1)+⋯ +f(xn−1)}+f(xn)]\begin{array}{r} \int_a^b f(x) \mathrm{d} x \approx \frac{b-a}{2 n}\left[f\left(x_0\right)+2\left\{f\left(x_1\right)+\cdots\right.\right. \left.\left.+f\left(x_{n-1}\right)\right\}+f\left(x_n\right)\right] \end{array}

1.16: ベクトルの微分 & 積分

  1. ベクトルの微分と積分：成分ごとに微分/積分する．あるいは無限に近い22つのベクトルの差を求めることで 微分す.
+ diff --git a/academic/physics/ipho-formulas-jpn/10.html b/academic/physics/ipho-formulas-jpn/10.html index 29adca08..b471d8db 100644 --- a/academic/physics/ipho-formulas-jpn/10.html +++ b/academic/physics/ipho-formulas-jpn/10.html @@ -8,7 +8,7 @@ - + @@ -49,8 +49,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​,ν=vnS.

10.10: Carnot サイクル

  1. Carnot サイクル : 断熱過程 2 つと等温過程 2 つ. S−TS-T 座標を用いることにより η=(T1−T2)/T1\eta=\left(T_1-T_2\right) / T_1 を得る.

10.11: ヒートポンプ

  1. ヒートポンプ: Carnot サイクルの逆. η=T1T1−T2\eta=\frac{T_1}{T_1-T_2}.

10.12: エントロピー

  1. エントロピー :dS=dQ/T: \mathrm{d} S=\mathrm{d} Q / T.

10.13: 熱力学第一法則

  1. 熱力学第一法則 : d′U=d′A+d′Q\mathrm{d}^{\prime} U=\mathrm{d}^{\prime} A+\mathrm{d}^{\prime} Q

10.14: 熱力学第二法則

  1. 熱力学第二法則 : ΔS≥0\Delta S \geq 0 (また ηreal ≤ηCarnot )\left.\eta_{\text {real }} \leq \eta_{\text {Carnot }}\right).

10.15: 気体のする仕事

  1. 気体のする仕事（ポイント 10 も参照）:

    A=∫p dV, 断熱過程: A=i2Δ(pV)A=\int p \mathrm{~d} V, \quad \text { 断熱過程: } A=\frac{i}{2} \Delta(p V)

10.16: Dalton の法則

  1. Dalton の法則: p=p= ∑pi\sum p_i

    訳者注

    理想気体のみ成立

10.17: 沸騰

  1. 沸騰: 飽和蒸気の圧力 pv=p0.2p_v=p_0 .2 液の界面では pv1+pv2=p0p_{v 1}+p_{v 2}=p_0.

10.18: 熱流

  1. 熱流: P=kSΔT/lP=k S \Delta T / l ( kk は熱伝導率). 直流回路に似て いる (P↔I,ΔT↔V,k↔1/ρ)(P \leftrightarrow I, \Delta T \leftrightarrow V, k \leftrightarrow 1 / \rho).

10.19: 熱容量

  1. 熱容量 : Q=∫c(T)dTQ=\int c(T) \mathrm{d} T. 固体では低温で c∝T3c \propto T^3, 高温で c=3NkBc=3 N k_B （Dulong-Petit の法則. ここで NN は結晶中の原子数）

10.20: 表面張力

  1. 表面張力 :

    U=Sσ,F=lσ,p=2σ/RU=S \sigma, F=l \sigma, p=2 \sigma / R

10.21: Stefan-Boltzmann の法則 (灰色体)

  1. Stefan-Boltzmann の法則 (灰色体) : P=εσAT4P=\varepsilon \sigma A T^4.

10.22: Wien の変位則

  1. Wien の変位則: νmax⁡=AkBT/h(A≈\nu_{\max }=A k_B T / h(A \approx 2.8), λmax⁡=hc/A′kBT(A′≈5)\lambda_{\max }=h c / A^{\prime} k_B T\left(A^{\prime} \approx 5\right).
- +M1001 80h400000v40h-400000z">​,ν=vnS.

10.10: Carnot サイクル

  1. Carnot サイクル : 断熱過程 2 つと等温過程 2 つ. S−TS-T 座標を用いることにより η=(T1−T2)/T1\eta=\left(T_1-T_2\right) / T_1 を得る.

10.11: ヒートポンプ

  1. ヒートポンプ: Carnot サイクルの逆. η=T1T1−T2\eta=\frac{T_1}{T_1-T_2}.

10.12: エントロピー

  1. エントロピー :dS=dQ/T: \mathrm{d} S=\mathrm{d} Q / T.

10.13: 熱力学第一法則

  1. 熱力学第一法則 : d′U=d′A+d′Q\mathrm{d}^{\prime} U=\mathrm{d}^{\prime} A+\mathrm{d}^{\prime} Q

10.14: 熱力学第二法則

  1. 熱力学第二法則 : ΔS≥0\Delta S \geq 0 (また ηreal ≤ηCarnot )\left.\eta_{\text {real }} \leq \eta_{\text {Carnot }}\right).

10.15: 気体のする仕事

  1. 気体のする仕事（ポイント 10 も参照）:

    A=∫p dV, 断熱過程: A=i2Δ(pV)A=\int p \mathrm{~d} V, \quad \text { 断熱過程: } A=\frac{i}{2} \Delta(p V)

10.16: Dalton の法則

  1. Dalton の法則: p=p= ∑pi\sum p_i

    訳者注

    理想気体のみ成立

10.17: 沸騰

  1. 沸騰: 飽和蒸気の圧力 pv=p0.2p_v=p_0 .2 液の界面では pv1+pv2=p0p_{v 1}+p_{v 2}=p_0.

10.18: 熱流

  1. 熱流: P=kSΔT/lP=k S \Delta T / l ( kk は熱伝導率). 直流回路に似て いる (P↔I,ΔT↔V,k↔1/ρ)(P \leftrightarrow I, \Delta T \leftrightarrow V, k \leftrightarrow 1 / \rho).

10.19: 熱容量

  1. 熱容量 : Q=∫c(T)dTQ=\int c(T) \mathrm{d} T. 固体では低温で c∝T3c \propto T^3, 高温で c=3NkBc=3 N k_B （Dulong-Petit の法則. ここで NN は結晶中の原子数）

10.20: 表面張力

  1. 表面張力 :

    U=Sσ,F=lσ,p=2σ/RU=S \sigma, F=l \sigma, p=2 \sigma / R

10.21: Stefan-Boltzmann の法則 (灰色体)

  1. Stefan-Boltzmann の法則 (灰色体) : P=εσAT4P=\varepsilon \sigma A T^4.

10.22: Wien の変位則

  1. Wien の変位則: νmax⁡=AkBT/h(A≈\nu_{\max }=A k_B T / h(A \approx 2.8), λmax⁡=hc/A′kBT(A′≈5)\lambda_{\max }=h c / A^{\prime} k_B T\left(A^{\prime} \approx 5\right).
+ diff --git a/academic/physics/ipho-formulas-jpn/11.html b/academic/physics/ipho-formulas-jpn/11.html index da882042..f09bd3b1 100644 --- a/academic/physics/ipho-formulas-jpn/11.html +++ b/academic/physics/ipho-formulas-jpn/11.html @@ -8,7 +8,7 @@ - + @@ -40,8 +40,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​) であれば容易に透過する.

11.7: Bohr モデル

  1. Bohr モデル : En∝−1/n2E_n \propto-1 / n^2. (古典的に計算される) 円軌道では, 軌道の長さが波長 λ=h/mv\lambda=h / m v の整数倍.

11.8: Compton 効果

  1. Compton 効果: 光子が電子から散乱されると, 光子の Δλ=λC(1−cos⁡θ)\Delta \lambda=\lambda_C(1-\cos \theta)

11.9: 光電効果

  1. 光電効果: W+mvmax⁡2/2=hνW+m v_{\max }^2 / 2=h \nu ( WW は仕事関数 )). I−VI-V グラフ：光電流は阻止電圧 V=−(hν−W)/eV=-(h \nu-W) / e で始まり, 正方向に電圧が大きくなると緩和する.

11.10: Stefan-Boltzmann の法則

  1. Stefan-Boltzmann の法則 : P=σAT4P=\sigma A T^4
- +M1001 80h400000v40h-400000z">​) であれば容易に透過する.

11.7: Bohr モデル

  1. Bohr モデル : En∝−1/n2E_n \propto-1 / n^2. (古典的に計算される) 円軌道では, 軌道の長さが波長 λ=h/mv\lambda=h / m v の整数倍.

11.8: Compton 効果

  1. Compton 効果: 光子が電子から散乱されると, 光子の Δλ=λC(1−cos⁡θ)\Delta \lambda=\lambda_C(1-\cos \theta)

11.9: 光電効果

  1. 光電効果: W+mvmax⁡2/2=hνW+m v_{\max }^2 / 2=h \nu ( WW は仕事関数 )). I−VI-V グラフ：光電流は阻止電圧 V=−(hν−W)/eV=-(h \nu-W) / e で始まり, 正方向に電圧が大きくなると緩和する.

11.10: Stefan-Boltzmann の法則

  1. Stefan-Boltzmann の法則 : P=σAT4P=\sigma A T^4
+ diff --git a/academic/physics/ipho-formulas-jpn/12.html b/academic/physics/ipho-formulas-jpn/12.html index b715bade..46c49846 100644 --- a/academic/physics/ipho-formulas-jpn/12.html +++ b/academic/physics/ipho-formulas-jpn/12.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Formulas for IPhO 日本語版: Section 12

12: Kepler の法則

12.1: F & U

  1. F=GMm/r2,U=−GMm/r. F=G M m / r^2, U=-G M m / r \text {. }

12.2: Kepler の第一法則

  1. Kepler の第一法則 (2 質点の重力相互作用)：それぞ れの軌道は，系の質量中心に焦点を持つ楕円，双曲線, 放物線になる. これは Runge-Lenz ベクトルから得ら れる (ポイント 9).

12.3: Kepler の第二法則

  1. Kepler の第二法則（角運動量の保存）: 中心力が働く 場にある質点について，その位置ベクトルは単位時間 に一定の面積を描く.

12.4: Kepler の第三法則

  1. Kepler の第三法則 :r−2: r^{-2} に比例する力が働く場で楕円 軌道を描く複数の質点について, 周期は長半径の 32\frac{3}{2} 乗 に比例する :

    T12/T22=a13/a23T_1^2 / T_2^2=a_1^3 / a_2^3

12.5: 楕円軌道

  1. 重力場中で楕円軌道を描く質点の全エネルギー (K+U)(K+U) :

    E=−GMm/2aE=-G M m / 2 a

12.6: 楕円率

  1. 楕円率が ε=d/a≪1\varepsilon=d / a \ll 1 の場合, 軌道は焦点をずらし た円形をしていると考えられる.

12.7: 楕円の性質

  1. 楕円の性質 :l1+l2=2a（l1: l_1+l_2=2 a （ l_1 と l2l_2 は焦点までの距 離). α1=α2\alpha_1=\alpha_2 (一方の焦点から出た光は他方の焦点に 反射する). S=πabS=\pi a b.

12.8: 円の中心

  1. 円とその円の中心に焦点をもつ楕円は長軸の部分での み接する.

12.9: nge-Lenz ベクトル

  1. Runge-Lenz ベクトル（楕円率ベクトル）[訳者注：こ のベクトルはむしろ離心率と関係する.そこでここで は離心率ベクトルとして知られるベクトルを代わりに 記す.これは焦点から近日点に向かう向きで，大きさ が離心率 ee に一致する.]：

    e=v×MGMm−er= const. \boldsymbol{e}=\frac{\boldsymbol{v} \times \boldsymbol{M}}{G M m}-\boldsymbol{e}_r=\text { const. }

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Formulas for IPhO 日本語版: Section 12

12: Kepler の法則

12.1: F & U

  1. F=GMm/r2,U=−GMm/r. F=G M m / r^2, U=-G M m / r \text {. }

12.2: Kepler の第一法則

  1. Kepler の第一法則 (2 質点の重力相互作用)：それぞ れの軌道は，系の質量中心に焦点を持つ楕円，双曲線, 放物線になる. これは Runge-Lenz ベクトルから得ら れる (ポイント 9).

12.3: Kepler の第二法則

  1. Kepler の第二法則（角運動量の保存）: 中心力が働く 場にある質点について，その位置ベクトルは単位時間 に一定の面積を描く.

12.4: Kepler の第三法則

  1. Kepler の第三法則 :r−2: r^{-2} に比例する力が働く場で楕円 軌道を描く複数の質点について, 周期は長半径の 32\frac{3}{2} 乗 に比例する :

    T12/T22=a13/a23T_1^2 / T_2^2=a_1^3 / a_2^3

12.5: 楕円軌道

  1. 重力場中で楕円軌道を描く質点の全エネルギー (K+U)(K+U) :

    E=−GMm/2aE=-G M m / 2 a

12.6: 楕円率

  1. 楕円率が ε=d/a≪1\varepsilon=d / a \ll 1 の場合, 軌道は焦点をずらし た円形をしていると考えられる.

12.7: 楕円の性質

  1. 楕円の性質 :l1+l2=2a（l1: l_1+l_2=2 a （ l_1 と l2l_2 は焦点までの距 離). α1=α2\alpha_1=\alpha_2 (一方の焦点から出た光は他方の焦点に 反射する). S=πabS=\pi a b.

12.8: 円の中心

  1. 円とその円の中心に焦点をもつ楕円は長軸の部分での み接する.

12.9: nge-Lenz ベクトル

  1. Runge-Lenz ベクトル（楕円率ベクトル）[訳者注：こ のベクトルはむしろ離心率と関係する.そこでここで は離心率ベクトルとして知られるベクトルを代わりに 記す.これは焦点から近日点に向かう向きで，大きさ が離心率 ee に一致する.]：

    e=v×MGMm−er= const. \boldsymbol{e}=\frac{\boldsymbol{v} \times \boldsymbol{M}}{G M m}-\boldsymbol{e}_r=\text { const. }

+ diff --git a/academic/physics/ipho-formulas-jpn/13.html b/academic/physics/ipho-formulas-jpn/13.html index d2f44675..bf522ca3 100644 --- a/academic/physics/ipho-formulas-jpn/13.html +++ b/academic/physics/ipho-formulas-jpn/13.html @@ -8,7 +8,7 @@ - + @@ -90,8 +90,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​

13.11: 電場と磁場の Lorentz 変換

  1. 電場と磁場の Lorentz 変換 : E∥′=E∥,B∥′=B∥\boldsymbol{E}_{\|}^{\prime}=\boldsymbol{E}_{\|}, \boldsymbol{B}_{\|}^{\prime}=\boldsymbol{B}_{\|},

    E⊥′/c=γ(E⊥/c+v/c×B⊥),B⊥′=γ(B⊥−v/c×E⊥/c)\begin{gathered} \boldsymbol{E}_{\perp}^{\prime} / c=\gamma\left(\boldsymbol{E}_{\perp} / c+\boldsymbol{v} / c \times \boldsymbol{B}_{\perp}\right), \\ \boldsymbol{B}_{\perp}^{\prime}=\gamma\left(\boldsymbol{B}_{\perp}-\boldsymbol{v} / c \times \boldsymbol{E}_{\perp} / c\right) \end{gathered}

- +M1001 80h400000v40h-400000z">​

13.11: 電場と磁場の Lorentz 変換

  1. 電場と磁場の Lorentz 変換 : E∥′=E∥,B∥′=B∥\boldsymbol{E}_{\|}^{\prime}=\boldsymbol{E}_{\|}, \boldsymbol{B}_{\|}^{\prime}=\boldsymbol{B}_{\|},

    E⊥′/c=γ(E⊥/c+v/c×B⊥),B⊥′=γ(B⊥−v/c×E⊥/c)\begin{gathered} \boldsymbol{E}_{\perp}^{\prime} / c=\gamma\left(\boldsymbol{E}_{\perp} / c+\boldsymbol{v} / c \times \boldsymbol{B}_{\perp}\right), \\ \boldsymbol{B}_{\perp}^{\prime}=\gamma\left(\boldsymbol{B}_{\perp}-\boldsymbol{v} / c \times \boldsymbol{E}_{\perp} / c\right) \end{gathered}

+ diff --git a/academic/physics/ipho-formulas-jpn/2.html b/academic/physics/ipho-formulas-jpn/2.html index 73f95e06..b16d564e 100644 --- a/academic/physics/ipho-formulas-jpn/2.html +++ b/academic/physics/ipho-formulas-jpn/2.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Formulas for IPhO 日本語版: Section 2

2: 一般的な推奨事

  1. 全ての計算式の正しさを確かめる：a) 次元を調べる. b) 簡単で特別な場合を調べる（2 つの変数が等しい, 1 つの変数が 0 または ∞\infty ). c) 解の定性的な挙動の妥当 性を調ベる. 2.もし問題文中に驚くベき偶然の一致があれば（例えば 2 つのものが同じ), 解答の鍵はそこにあるかもしれ ない.
  2. 問題文中の推奨事項をよく読む. 些細な部分に重要な 情報が含まれている場合があるので，問題文の文言に 注意する. かなり時間をかけても問題が解けない場合 は, 問題を誤解しているかもしれないので, もう一度 問題文を読む.
  3. 長くて時間のかかる計算は, 簡略化しなければならな い始めの方程式を全て書き出したのち, 最後（他の全 てが終わったとき) まで先送りする.
  4. 絶望的に難しいと思われる問題でも，たいてい非常に シンプルな解法がある.オリンピックの問題に限って 言えば，絶対に解ける.
  5. 実験では, a) 測定するほどの時問が無いとしても, 実 験計画の概略を書く，b) 結果の正確さを高める方法を 考える，c) 測定した值を全て（表として）書き出す.
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Formulas for IPhO 日本語版: Section 2

2: 一般的な推奨事

  1. 全ての計算式の正しさを確かめる：a) 次元を調べる. b) 簡単で特別な場合を調べる（2 つの変数が等しい, 1 つの変数が 0 または ∞\infty ). c) 解の定性的な挙動の妥当 性を調ベる. 2.もし問題文中に驚くベき偶然の一致があれば（例えば 2 つのものが同じ), 解答の鍵はそこにあるかもしれ ない.
  2. 問題文中の推奨事項をよく読む. 些細な部分に重要な 情報が含まれている場合があるので，問題文の文言に 注意する. かなり時間をかけても問題が解けない場合 は, 問題を誤解しているかもしれないので, もう一度 問題文を読む.
  3. 長くて時間のかかる計算は, 簡略化しなければならな い始めの方程式を全て書き出したのち, 最後（他の全 てが終わったとき) まで先送りする.
  4. 絶望的に難しいと思われる問題でも，たいてい非常に シンプルな解法がある.オリンピックの問題に限って 言えば，絶対に解ける.
  5. 実験では, a) 測定するほどの時問が無いとしても, 実 験計画の概略を書く，b) 結果の正確さを高める方法を 考える，c) 測定した值を全て（表として）書き出す.
+ diff --git a/academic/physics/ipho-formulas-jpn/3.html b/academic/physics/ipho-formulas-jpn/3.html index 91370538..401cbba1 100644 --- a/academic/physics/ipho-formulas-jpn/3.html +++ b/academic/physics/ipho-formulas-jpn/3.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Formulas for IPhO 日本語版: Section 3

3: 運動学

3.1: 質点

  1. 質点または剛体の並進運動の場合（積分 → グラフの下 の面積）：

    v=dxdt,x=∫vdt(x=∫vx dt など )a=dvdt=d2xdt2,v=∫adtt=∫vx−1 dx=∫ax−1 dvx,x=∫vxax dvx\begin{gathered} \boldsymbol{v}=\frac{\mathrm{d} \boldsymbol{x}}{\mathrm{d} t}, \boldsymbol{x}=\int \boldsymbol{v} \mathrm{d} t\left(x=\int v_x \mathrm{~d} t \text { など }\right) \\ \boldsymbol{a}=\frac{\mathrm{d} \boldsymbol{v}}{\mathrm{d} t}=\frac{\mathrm{d}^2 \boldsymbol{x}}{\mathrm{d} t^2}, \boldsymbol{v}=\int \boldsymbol{a} \mathrm{d} t \\ t=\int v_x^{-1} \mathrm{~d} x=\int a_x^{-1} \mathrm{~d} v_x, x=\int \frac{v_x}{a_x} \mathrm{~d} v_x \end{gathered}

    もし aa が定数ならば, これらの積分は簡単に求めるこ とができて, 例えば

    x=v0t+at2/2=(v2−v02)/2a. x=v_0 t+a t^2 / 2=\left(v^2-v_0^2\right) / 2 a \text {. }

3.2: 回転運動

  1. 回転運動は, 並進運動と似ていて：

    ω=dφ/dt,ε=dω/dta=τdv/dt+nv2/R\begin{aligned} \omega & =\mathrm{d} \varphi / \mathrm{d} t, \varepsilon=\mathrm{d} \omega / \mathrm{d} t \\ \boldsymbol{a} & =\boldsymbol{\tau} \mathrm{d} v / \mathrm{d} t+\boldsymbol{n} v^2 / R \end{aligned}

3.3: 曲線運動

  1. 曲線運動は，ポイント 1 と同じだが，ベクトルは線速 度，加速度，経路長に置き換える.

3.4: 剛体の運動

  1. 剛体の運動:
    • vAcos⁡α=vBcos⁡βv_A \cos \alpha=v_B \cos \beta ここで, vA\boldsymbol{v}_A と vB\boldsymbol{v}_B は剛体上の点 AA と BB の速度, α\alpha と β\beta は vA\boldsymbol{v}_A と vB\boldsymbol{v}_B が直線 ABA B となす角.
    • 瞬間回転中心 (#質点の軌道 の曲率中心）は, a\boldsymbol{a} と b\boldsymbol{b} に下ろした垂線の交点. 又は もし vA,vB⊥AB\boldsymbol{v}_A, \boldsymbol{v}_B \perp A B ならば, vA\boldsymbol{v}_A と vB\boldsymbol{v}_B の先端を結ぶ 直線と ABA B の交点.

3.5: 非慣性系

  1. 非慣性系：

    v2=v0+v1,a2=a0+a1+ω2R+aCor ここで, aCor⊥v1. もし v1=0 なら aCor=0.\begin{array}{r} \quad \boldsymbol{v}_2=\boldsymbol{v}_0+\boldsymbol{v}_1, \boldsymbol{a}_2=\boldsymbol{a}_0+\boldsymbol{a}_1+\omega^2 \boldsymbol{R}+\boldsymbol{a}_{C o r} \\ \text { ここで, } \boldsymbol{a}_{C o r} \perp \boldsymbol{v}_1 . \text { もし } \boldsymbol{v}_1=0 \text { なら } \boldsymbol{a}_{C o r}=0 . \end{array}

3.6: 弾道問題

  1. 弾道問題：到達可能な範囲は

    y≤v02/(2g)−gx2/(2v02)y \leq v_0^2 /(2 g)-g x^2 /\left(2 v_0^2\right)

    最適な弾道では, 初速度と終速（衝突時の速度）が垂直 になる.

3.7: 最短経路

  1. 最短経路を求めるには，Fermat と Huygens の原理が 使える.

3.8: ベクトル

  1. ベクトル（速度，加速度）を求めるには，その向きと （場合によっては傾いた）ある軸への射影を求めれば 充分.
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Formulas for IPhO 日本語版: Section 3

3: 運動学

3.1: 質点

  1. 質点または剛体の並進運動の場合（積分 → グラフの下 の面積）：

    v=dxdt,x=∫vdt(x=∫vx dt など )a=dvdt=d2xdt2,v=∫adtt=∫vx−1 dx=∫ax−1 dvx,x=∫vxax dvx\begin{gathered} \boldsymbol{v}=\frac{\mathrm{d} \boldsymbol{x}}{\mathrm{d} t}, \boldsymbol{x}=\int \boldsymbol{v} \mathrm{d} t\left(x=\int v_x \mathrm{~d} t \text { など }\right) \\ \boldsymbol{a}=\frac{\mathrm{d} \boldsymbol{v}}{\mathrm{d} t}=\frac{\mathrm{d}^2 \boldsymbol{x}}{\mathrm{d} t^2}, \boldsymbol{v}=\int \boldsymbol{a} \mathrm{d} t \\ t=\int v_x^{-1} \mathrm{~d} x=\int a_x^{-1} \mathrm{~d} v_x, x=\int \frac{v_x}{a_x} \mathrm{~d} v_x \end{gathered}

    もし aa が定数ならば, これらの積分は簡単に求めるこ とができて, 例えば

    x=v0t+at2/2=(v2−v02)/2a. x=v_0 t+a t^2 / 2=\left(v^2-v_0^2\right) / 2 a \text {. }

3.2: 回転運動

  1. 回転運動は, 並進運動と似ていて：

    ω=dφ/dt,ε=dω/dta=τdv/dt+nv2/R\begin{aligned} \omega & =\mathrm{d} \varphi / \mathrm{d} t, \varepsilon=\mathrm{d} \omega / \mathrm{d} t \\ \boldsymbol{a} & =\boldsymbol{\tau} \mathrm{d} v / \mathrm{d} t+\boldsymbol{n} v^2 / R \end{aligned}

3.3: 曲線運動

  1. 曲線運動は，ポイント 1 と同じだが，ベクトルは線速 度，加速度，経路長に置き換える.

3.4: 剛体の運動

  1. 剛体の運動:
    • vAcos⁡α=vBcos⁡βv_A \cos \alpha=v_B \cos \beta ここで, vA\boldsymbol{v}_A と vB\boldsymbol{v}_B は剛体上の点 AA と BB の速度, α\alpha と β\beta は vA\boldsymbol{v}_A と vB\boldsymbol{v}_B が直線 ABA B となす角.
    • 瞬間回転中心 (#質点の軌道 の曲率中心）は, a\boldsymbol{a} と b\boldsymbol{b} に下ろした垂線の交点. 又は もし vA,vB⊥AB\boldsymbol{v}_A, \boldsymbol{v}_B \perp A B ならば, vA\boldsymbol{v}_A と vB\boldsymbol{v}_B の先端を結ぶ 直線と ABA B の交点.

3.5: 非慣性系

  1. 非慣性系：

    v2=v0+v1,a2=a0+a1+ω2R+aCor ここで, aCor⊥v1. もし v1=0 なら aCor=0.\begin{array}{r} \quad \boldsymbol{v}_2=\boldsymbol{v}_0+\boldsymbol{v}_1, \boldsymbol{a}_2=\boldsymbol{a}_0+\boldsymbol{a}_1+\omega^2 \boldsymbol{R}+\boldsymbol{a}_{C o r} \\ \text { ここで, } \boldsymbol{a}_{C o r} \perp \boldsymbol{v}_1 . \text { もし } \boldsymbol{v}_1=0 \text { なら } \boldsymbol{a}_{C o r}=0 . \end{array}

3.6: 弾道問題

  1. 弾道問題：到達可能な範囲は

    y≤v02/(2g)−gx2/(2v02)y \leq v_0^2 /(2 g)-g x^2 /\left(2 v_0^2\right)

    最適な弾道では, 初速度と終速（衝突時の速度）が垂直 になる.

3.7: 最短経路

  1. 最短経路を求めるには，Fermat と Huygens の原理が 使える.

3.8: ベクトル

  1. ベクトル（速度，加速度）を求めるには，その向きと （場合によっては傾いた）ある軸への射影を求めれば 充分.
+ diff --git a/academic/physics/ipho-formulas-jpn/4.html b/academic/physics/ipho-formulas-jpn/4.html index 105a35e2..0835654b 100644 --- a/academic/physics/ipho-formulas-jpn/4.html +++ b/academic/physics/ipho-formulas-jpn/4.html @@ -8,7 +8,7 @@ - + @@ -39,8 +39,8 @@ c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30 c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5 c53.7,-170.3,84.5,-266.8,92.5,-289.5z -M1001 80h400000v40h-400000z">​,l~=l+Ic​/ml​

4.12: 慣性モーメントの係数

  1. 慣性モーメントの係数 : 円柱 12\frac{1}{2}, 球 25\frac{2}{5}, 球殼 23\frac{2}{3}, 棒 112\frac{1}{12} （端に対しては 13\frac{1}{3} ), 正方形 16\frac{1}{6}.

4.13: よく使われる保存則

  1. よく使われる保存則：エネルギー（弾性衝突，摩擦な し), 運動量（正味の外力なし, 各方向について成立), 角運動量（正味の外トルクなし, 例えば, 外力のうでの 長さが 0 (これが 2 又は 3 点のまわりに成り立てば運 動量保存で代用できる))

4.14: 非慣性系における見かけの力

  1. 非慣性系における見かけの力 : 慣性力 −ma-m a, 遠心力 mω2Rm \omega^2 \boldsymbol{R}, Coriolis 力 2mv×Ω2 m \boldsymbol{v} \times \Omega (避けた方がよい. 速 度に垂直なので仕事はしない).

4.15: 傾いた座標

  1. 傾いた座標：斜面上での運動については, 斜面に平行 と垂直な方向に軸をとるのがよい。このとき重力加速 度は xx 成分と yy 成分をもつ. 軸は斜交することもある が, v=vxex+vyey\boldsymbol{v}=v_x \boldsymbol{e}_x+v_y \boldsymbol{e}_y のとき vxv_x は v\boldsymbol{v} の xx 軸への射 影ではない.

4.16: 2 つの物体の衝突

  1. 2 つの物体の衝突 : 保存されるのは, a) 全運動量, b) 全角運動量，c) 一方の物体の衝突点に関する角運動量, d) 全エネルギー（弾性衝突の場合， 摩擦がある場合 は, 摩擦力に垂直な方向の運動エネルギーが保存される. e) 衝突中に滑りが止まったならば，接触点の最終 速度は接触面上にある. f) 滑りが止まらなかったなら ば, 一方の物体から他方に伝わる運動量は, 接触面の 法線と arctan⁡μ\arctan \mu の角度をなす.

4.17: 剛体のすべての運動

  1. 剛体のすべての運動は (物体の各点の速度を見ると) 瞬 間回転中心 CC まわりの回転として表せる. 物体上の点 PP の CC からの距離は PP の軌跡の曲率半径とは異なる ことに注意せよ.

4.18: 紐の張力

  1. 紐の張力：重さのある吊り紐では, 張力の水平成分は 一定で垂直成分は下にある紐の重さにより変わる. 滑 らかな面の上の紐による（単位長さあたりの）力は，そ の曲率半径と張力で決まり, N=T/RN=T / R. 似た場合と して, 表面張力による圧力は p=2σ/Rp=2 \sigma / R. 導出には直 径に沿った圧力を調ベる.

4.19: 液体の表面

  1. 液体の表面は（表面張力を無視すれば）等ポテンシャ ル面になる. 非圧縮性流体では, ww をポテンシャルエ ネルギーの体積密度として, p=P0−wp=P_0-w.

4.20: 非圧縮性流体に対する Bernoulli の法則

  1. 非圧縮性流体に対する Bernoulli の法則：

    p+12ρv2+ρϕ= const. p+\frac{1}{2} \rho v^2+\rho \phi=\text { const. }

    一様な重力場では ϕ=gh\phi=g h. 比熱が cp[ J/kg]c_p[\mathrm{~J} / \mathrm{kg}] である気 体では,

    12v2+cpT= const. \frac{1}{2} v^2+c_p T=\text { const. }

4.21: 直線的な流線

  1. 直線的な流線に沾う運動量の連続性 : p+ρv2=p+\rho v^2= const.

4.22: 断熱不変量

  1. 断熱不変量 : 振動する系の 1 周期の間のパラメータの 相対的な変化が小さければ，位相空間（ x−px-p 座標で表さ れる）上に書かれるループの面積は非常に高い精度で 保存される.

4.23: 安定性

  1. 安定性を調ベるには, a) ポテンシャルエネルギー最小 の原理，又は b) 仮想仕事の原理を用いる.

4.24: 空間的に有限な運動に対する Virial 定理

  1. 空間的に有限な運動に対する Virial 定理：a) もし F∝∣r∣F \propto|\boldsymbol{r}| ならば ⟨K⟩=⟨U⟩\langle K\rangle=\langle U\rangle (時間平均). b) もし F∝∣r∣−2F \propto|\boldsymbol{r}|^{-2} ならば 2⟨K⟩=−⟨U⟩2\langle K\rangle=-\langle U\rangle.

4.25: Tsiolkovsky 公式

  1. Tsiolkovsky の公式（ロケット）: Δv=uln⁡Mm\Delta v=u \ln \frac{M}{m}
- +M1001 80h400000v40h-400000z">​,l~=l+Ic​/ml​

4.12: 慣性モーメントの係数

  1. 慣性モーメントの係数 : 円柱 12\frac{1}{2}, 球 25\frac{2}{5}, 球殼 23\frac{2}{3}, 棒 112\frac{1}{12} （端に対しては 13\frac{1}{3} ), 正方形 16\frac{1}{6}.

4.13: よく使われる保存則

  1. よく使われる保存則：エネルギー（弾性衝突，摩擦な し), 運動量（正味の外力なし, 各方向について成立), 角運動量（正味の外トルクなし, 例えば, 外力のうでの 長さが 0 (これが 2 又は 3 点のまわりに成り立てば運 動量保存で代用できる))

4.14: 非慣性系における見かけの力

  1. 非慣性系における見かけの力 : 慣性力 −ma-m a, 遠心力 mω2Rm \omega^2 \boldsymbol{R}, Coriolis 力 2mv×Ω2 m \boldsymbol{v} \times \Omega (避けた方がよい. 速 度に垂直なので仕事はしない).

4.15: 傾いた座標

  1. 傾いた座標：斜面上での運動については, 斜面に平行 と垂直な方向に軸をとるのがよい。このとき重力加速 度は xx 成分と yy 成分をもつ. 軸は斜交することもある が, v=vxex+vyey\boldsymbol{v}=v_x \boldsymbol{e}_x+v_y \boldsymbol{e}_y のとき vxv_x は v\boldsymbol{v} の xx 軸への射 影ではない.

4.16: 2 つの物体の衝突

  1. 2 つの物体の衝突 : 保存されるのは, a) 全運動量, b) 全角運動量，c) 一方の物体の衝突点に関する角運動量, d) 全エネルギー（弾性衝突の場合， 摩擦がある場合 は, 摩擦力に垂直な方向の運動エネルギーが保存される. e) 衝突中に滑りが止まったならば，接触点の最終 速度は接触面上にある. f) 滑りが止まらなかったなら ば, 一方の物体から他方に伝わる運動量は, 接触面の 法線と arctan⁡μ\arctan \mu の角度をなす.

4.17: 剛体のすべての運動

  1. 剛体のすべての運動は (物体の各点の速度を見ると) 瞬 間回転中心 CC まわりの回転として表せる. 物体上の点 PP の CC からの距離は PP の軌跡の曲率半径とは異なる ことに注意せよ.

4.18: 紐の張力

  1. 紐の張力：重さのある吊り紐では, 張力の水平成分は 一定で垂直成分は下にある紐の重さにより変わる. 滑 らかな面の上の紐による（単位長さあたりの）力は，そ の曲率半径と張力で決まり, N=T/RN=T / R. 似た場合と して, 表面張力による圧力は p=2σ/Rp=2 \sigma / R. 導出には直 径に沿った圧力を調ベる.

4.19: 液体の表面

  1. 液体の表面は（表面張力を無視すれば）等ポテンシャ ル面になる. 非圧縮性流体では, ww をポテンシャルエ ネルギーの体積密度として, p=P0−wp=P_0-w.

4.20: 非圧縮性流体に対する Bernoulli の法則

  1. 非圧縮性流体に対する Bernoulli の法則：

    p+12ρv2+ρϕ= const. p+\frac{1}{2} \rho v^2+\rho \phi=\text { const. }

    一様な重力場では ϕ=gh\phi=g h. 比熱が cp[ J/kg]c_p[\mathrm{~J} / \mathrm{kg}] である気 体では,

    12v2+cpT= const. \frac{1}{2} v^2+c_p T=\text { const. }

4.21: 直線的な流線

  1. 直線的な流線に沾う運動量の連続性 : p+ρv2=p+\rho v^2= const.

4.22: 断熱不変量

  1. 断熱不変量 : 振動する系の 1 周期の間のパラメータの 相対的な変化が小さければ，位相空間（ x−px-p 座標で表さ れる）上に書かれるループの面積は非常に高い精度で 保存される.

4.23: 安定性

  1. 安定性を調ベるには, a) ポテンシャルエネルギー最小 の原理，又は b) 仮想仕事の原理を用いる.

4.24: 空間的に有限な運動に対する Virial 定理

  1. 空間的に有限な運動に対する Virial 定理：a) もし F∝∣r∣F \propto|\boldsymbol{r}| ならば ⟨K⟩=⟨U⟩\langle K\rangle=\langle U\rangle (時間平均). b) もし F∝∣r∣−2F \propto|\boldsymbol{r}|^{-2} ならば 2⟨K⟩=−⟨U⟩2\langle K\rangle=-\langle U\rangle.

4.25: Tsiolkovsky 公式

  1. Tsiolkovsky の公式（ロケット）: Δv=uln⁡Mm\Delta v=u \ln \frac{M}{m}
+ diff --git a/academic/physics/ipho-formulas-jpn/5.html b/academic/physics/ipho-formulas-jpn/5.html index b62cfaca..c46ffa4d 100644 --- a/academic/physics/ipho-formulas-jpn/5.html +++ b/academic/physics/ipho-formulas-jpn/5.html @@ -8,7 +8,7 @@ - + @@ -99,8 +99,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​.

5.10: Doppler 効果

  1. Doppler 効果 : ν=ν01+v∥/cs1−u∥/cs\nu=\nu_0 \frac{1+v_{\|} / c_s}{1-u_{\|} / c_s}.

5.11: Huygens の原理

  1. Huygens の原理 : 波面は段階的に構成される. 過去 の波面のすべての点に仮想的な波源を置く. 結果は距 離 Δx=csΔt\Delta x=c_s \Delta t で区切られた曲線（ここで Δt\Delta t は時間 間隔， csc_s は与えられた点の速度). 波は波面に垂直に 進む.
- +M1001 80h400000v40h-400000z">​.

5.10: Doppler 効果

  1. Doppler 効果 : ν=ν01+v∥/cs1−u∥/cs\nu=\nu_0 \frac{1+v_{\|} / c_s}{1-u_{\|} / c_s}.

5.11: Huygens の原理

  1. Huygens の原理 : 波面は段階的に構成される. 過去 の波面のすべての点に仮想的な波源を置く. 結果は距 離 Δx=csΔt\Delta x=c_s \Delta t で区切られた曲線（ここで Δt\Delta t は時間 間隔， csc_s は与えられた点の速度). 波は波面に垂直に 進む.
+ diff --git a/academic/physics/ipho-formulas-jpn/6.html b/academic/physics/ipho-formulas-jpn/6.html index 4656d74d..9d2b05d5 100644 --- a/academic/physics/ipho-formulas-jpn/6.html +++ b/academic/physics/ipho-formulas-jpn/6.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Formulas for IPhO 日本語版: Section 6

6: 幾何光学，測光

6.1: Fermat 原理

  1. Fermat の原理 : 点 AA から BB への波の経路は波の移動 時間が最も短いもの.

6.2: Snell 法則

  1. Snell の法則 :

sin⁡α1/sin⁡α2=n2/n1=v1/v2.\sin \alpha_1 / \sin \alpha_2=n_2 / n_1=v_1 / v_2 .

6.3: 屈折率

  1. 屈折率が連続的に変化するならば，媒質を屈折率が nn で一定のいくつかの仮想的な層に分けて Snell の 法則を適用する. 光線は屈折率一定の層に沿って進む こともでき,もし全反射の条件をわずかに満たせば, n′=n/r(rn^{\prime}=n / r \quad(r は曲率半径 ))

6.4: 屈折率な座標

  1. 屈折率が z\mathrm{z} 座標にのみ依存するならば, 光子の運動量 px,pyp_x, p_y とエネルギーは保存される:

kx,ky= const., ∣k∣/n= const. k_x, k_y=\text { const., }|\boldsymbol{k}| / n=\text { const. }

6.5:薄いレンズの式

  1. 薄いレンズの式（符号に注意する）：

1/a+1/b=1/f≡D1 / a+1 / b=1 / f \equiv D

6.6: Newton の式

  1. Newton の式 : 物体側焦点から物体までの距離を x1x_1, 像側焦点から像までの距離を x2x_2 とすると, x1x2=f2x_1 x_2=f^2

6.7: 像の位置を求める視差法

  1. 像の位置を求める視差法 : 目の位置と垂直に動かした ときに，鉛筆の先が像に対してずれないような位置を 探す.

6.8: レンズを通る光線の経路の幾何学的な描き方

  1. レンズを通る光線の経路の幾何学的な描き方：a) レン ズの中心を通る光線は屈折しない。b) 光軸に平行な光 線は焦点を通る，c) 屈折後, 初めに平行だった光線どうしは焦点面（焦点を通り光軸に垂直な平面）上で集 まる．d) 平面の像は平面であり，この 2 つの平面はレ ンズの平面上で交わる．

6.9: 光束

  1. 光束 Φ\Phi [単位: lumen (lm⁡)(\operatorname{lm})] は, 光のエネルギー を示し, 眼の感度に応じて重み付けされる. 光度 [candela (cd)]は（光源から出る）立体角あたりの 光束で, I=Φ/ΩI=\Phi / \Omega. 照度 [lux⁡(lx)][\operatorname{lux}(\mathrm{lx})] は（面に入射する） 面積あたりの光束で, E=Φ/SE=\Phi / S.

6.10: Gauss 定理

  1. 光束についての Gauss の定理 : 光度 IiI_i の点光源を囲 む閉曲面を通って外に出る光束は, Φ=4π∑Ii\Phi=4 \pi \sum I_i. 光 源が 1 つで距離が rr のとき E=I/r2E=I / r^2

6.11: 実験のヒント

  1. 実験のヒント：紙についた油污れが周囲の紙と同じ明 るさならば，その紙は両面から同じように照らされて いる.
- +
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Formulas for IPhO 日本語版: Section 6

6: 幾何光学，測光

6.1: Fermat 原理

  1. Fermat の原理 : 点 AA から BB への波の経路は波の移動 時間が最も短いもの.

6.2: Snell 法則

  1. Snell の法則 :

sin⁡α1/sin⁡α2=n2/n1=v1/v2.\sin \alpha_1 / \sin \alpha_2=n_2 / n_1=v_1 / v_2 .

6.3: 屈折率

  1. 屈折率が連続的に変化するならば，媒質を屈折率が nn で一定のいくつかの仮想的な層に分けて Snell の 法則を適用する. 光線は屈折率一定の層に沿って進む こともでき,もし全反射の条件をわずかに満たせば, n′=n/r(rn^{\prime}=n / r \quad(r は曲率半径 ))

6.4: 屈折率な座標

  1. 屈折率が z\mathrm{z} 座標にのみ依存するならば, 光子の運動量 px,pyp_x, p_y とエネルギーは保存される:

kx,ky= const., ∣k∣/n= const. k_x, k_y=\text { const., }|\boldsymbol{k}| / n=\text { const. }

6.5:薄いレンズの式

  1. 薄いレンズの式（符号に注意する）：

1/a+1/b=1/f≡D1 / a+1 / b=1 / f \equiv D

6.6: Newton の式

  1. Newton の式 : 物体側焦点から物体までの距離を x1x_1, 像側焦点から像までの距離を x2x_2 とすると, x1x2=f2x_1 x_2=f^2

6.7: 像の位置を求める視差法

  1. 像の位置を求める視差法 : 目の位置と垂直に動かした ときに，鉛筆の先が像に対してずれないような位置を 探す.

6.8: レンズを通る光線の経路の幾何学的な描き方

  1. レンズを通る光線の経路の幾何学的な描き方：a) レン ズの中心を通る光線は屈折しない。b) 光軸に平行な光 線は焦点を通る，c) 屈折後, 初めに平行だった光線どうしは焦点面（焦点を通り光軸に垂直な平面）上で集 まる．d) 平面の像は平面であり，この 2 つの平面はレ ンズの平面上で交わる．

6.9: 光束

  1. 光束 Φ\Phi [単位: lumen (lm⁡)(\operatorname{lm})] は, 光のエネルギー を示し, 眼の感度に応じて重み付けされる. 光度 [candela (cd)]は（光源から出る）立体角あたりの 光束で, I=Φ/ΩI=\Phi / \Omega. 照度 [lux⁡(lx)][\operatorname{lux}(\mathrm{lx})] は（面に入射する） 面積あたりの光束で, E=Φ/SE=\Phi / S.

6.10: Gauss 定理

  1. 光束についての Gauss の定理 : 光度 IiI_i の点光源を囲 む閉曲面を通って外に出る光束は, Φ=4π∑Ii\Phi=4 \pi \sum I_i. 光 源が 1 つで距離が rr のとき E=I/r2E=I / r^2

6.11: 実験のヒント

  1. 実験のヒント：紙についた油污れが周囲の紙と同じ明 るさならば，その紙は両面から同じように照らされて いる.
+ diff --git a/academic/physics/ipho-formulas-jpn/7.html b/academic/physics/ipho-formulas-jpn/7.html index 4e237d39..81709fab 100644 --- a/academic/physics/ipho-formulas-jpn/7.html +++ b/academic/physics/ipho-formulas-jpn/7.html @@ -8,7 +8,7 @@ - + @@ -40,8 +40,8 @@ s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5, c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1 s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26 c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z -M1001 80h400000v40h-400000z">​ (普通 μ≈1\mu \approx 1 ) であることに注意せよ. エネ ルギー流密度（単位面積を通過する単位時間あたりの エネルギー）: I=cnε0E2=cnμ0B2(EI=c n \varepsilon_0 E^2=\frac{c}{n \mu_0} B^2(E と BB は実 効值)

7.12: Malus の法則

  1. Malus の法則 : 直線偏光が角度 φ\varphi で偏光板を通過する と I=I0cos⁡2φI=I_0 \cos ^2 \varphi

7.13: 1/4 波長版

  1. 1/41 / 4 波長版 : 直線偏光成分間の位相が π/2\pi / 2 ずれる.

7.14: Brewster 角

  1. Brewster 角: 入射角が tan⁡φ=n\tan \varphi=n を満たすとき, 反 射波と屈折波が垂直になり反射波は直線偏光となる.

7.15: 光学素子による回折

  1. 光学素子による回折 : レンズやプリズムなどを通る光 の光学距離を計算する必要はなく, 図形的に考える. 例えば，双プリズムは二重スリットによる回折と同じ 回折をする.

7.16: 光ファイバー

  1. 光ファイバー：Mach-Zehnder 干渉計は二重スリッ トによる干渉と, 円形共振器は Fabry-Pérot 干渉計 と似ている. Bragg フィルターは X\mathrm{X} 線の場合と同 じように働く. シングルモードの光ファイバーでは, Δn/n≈12(λ/d)2\Delta n / n \approx \frac{1}{2}(\lambda / d)^2.
- +M1001 80h400000v40h-400000z">​ (普通 μ≈1\mu \approx 1 ) であることに注意せよ. エネ ルギー流密度（単位面積を通過する単位時間あたりの エネルギー）: I=cnε0E2=cnμ0B2(EI=c n \varepsilon_0 E^2=\frac{c}{n \mu_0} B^2(E と BB は実 効值)

7.12: Malus の法則

  1. Malus の法則 : 直線偏光が角度 φ\varphi で偏光板を通過する と I=I0cos⁡2φI=I_0 \cos ^2 \varphi

7.13: 1/4 波長版

  1. 1/41 / 4 波長版 : 直線偏光成分間の位相が π/2\pi / 2 ずれる.

7.14: Brewster 角

  1. Brewster 角: 入射角が tan⁡φ=n\tan \varphi=n を満たすとき, 反 射波と屈折波が垂直になり反射波は直線偏光となる.

7.15: 光学素子による回折

  1. 光学素子による回折 : レンズやプリズムなどを通る光 の光学距離を計算する必要はなく, 図形的に考える. 例えば，双プリズムは二重スリットによる回折と同じ 回折をする.

7.16: 光ファイバー

  1. 光ファイバー：Mach-Zehnder 干渉計は二重スリッ トによる干渉と, 円形共振器は Fabry-Pérot 干渉計 と似ている. Bragg フィルターは X\mathrm{X} 線の場合と同 じように働く. シングルモードの光ファイバーでは, Δn/n≈12(λ/d)2\Delta n / n \approx \frac{1}{2}(\lambda / d)^2.
+ diff --git a/academic/physics/ipho-formulas-jpn/8.html b/academic/physics/ipho-formulas-jpn/8.html index 32826ae8..2cdba664 100644 --- a/academic/physics/ipho-formulas-jpn/8.html +++ b/academic/physics/ipho-formulas-jpn/8.html @@ -8,7 +8,7 @@ - + @@ -52,8 +52,8 @@ c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z -M834 80h400000v40h-400000z">​ が成立. - +M834 80h400000v40h-400000z">​ が成立. + diff --git a/academic/physics/ipho-formulas-jpn/9.html b/academic/physics/ipho-formulas-jpn/9.html index 32a38fca..a98101b4 100644 --- a/academic/physics/ipho-formulas-jpn/9.html +++ b/academic/physics/ipho-formulas-jpn/9.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Formulas for IPhO 日本語版: Section 9

9: 電磁気学

9.1: Coulomb の法則

  1. F=kq1q2/r2,U=kq1q2/rF=k q_1 q_2 / r^2, U=k q_1 q_2 / r で, Kepler の法則が 使える (Section 12 参照).

9.2: Gauss の法則

  1. Gauss の法則 : ∮B⋅dS=0\oint \boldsymbol{B} \cdot \mathrm{d} \boldsymbol{S}=0,

    ∮εE⋅dS=Q,∮g⋅dS=−4πGM\oint \varepsilon \boldsymbol{E} \cdot \mathrm{d} \boldsymbol{S}=Q, \oint \boldsymbol{g} \cdot \mathrm{d} \boldsymbol{S}=-4 \pi G M

9.3: 循環定理

  1. 循環定理 :

    ∮E⋅dl=0(=Φ˙),∮B⋅dlμ=I,∮g⋅dl=0\oint \boldsymbol{E} \cdot \mathrm{d} \boldsymbol{l}=0(=\dot{\Phi}), \oint \frac{\boldsymbol{B} \cdot \mathrm{d} \boldsymbol{l}}{\mu}=I, \oint \boldsymbol{g} \cdot \mathrm{d} \boldsymbol{l}=0

9.4: 電流素片により生じる磁束密度

  1. 電流素片により生じる磁束密度 :

    dB=μI4πdl×err2.\mathrm{d} \boldsymbol{B}=\frac{\mu I}{4 \pi} \frac{\mathrm{d} \boldsymbol{l} \times \boldsymbol{e}_r}{r^2} .

    したがって電流 II が流れる円形回路の中心では B=μ0I2rB=\frac{\mu_0 I}{2 r}.

9.5: ローレンツ力

  1. F=e(E+v×B),F=I×Bl\boldsymbol{F}=e(\boldsymbol{E}+\boldsymbol{v} \times \boldsymbol{B}), \boldsymbol{F}=\boldsymbol{I} \times \boldsymbol{B} l.

9.6: Gauss の定理と循環定理より

  1. Gauss の定理と循環定理より：帯電した導線について E=σ2πε0rE=\frac{\sigma}{2 \pi \varepsilon_0 r}, 電流が流れる導線について B=μ0I2πrB=\frac{\mu_0 I}{2 \pi r}. 帯電した面について E=σ2ε0E=\frac{\sigma}{2 \varepsilon_0}, 電流が流れる面につい て B=μ0i2B=\frac{\mu_0 i}{2}. 一様に帯電した球殼（又は無限に長い円 筒）の内部で E=0E=0, 軸に沿って表面に電流が流れる 円筒の内部で B=0B=0. 密度 ρ\rho で一様に帯電, 又は一様 な電流 i\boldsymbol{i} が流れる, 球 (d=3)/(d=3) / 円柱 (d−2)/(d-2) / 平面 (d=1)(d=1) の内部で,

    E=ρεdr,B=1μdi×r\boldsymbol{E}=\frac{\rho}{\varepsilon d} \boldsymbol{r}, \boldsymbol{B}=\frac{1}{\mu d} \boldsymbol{i} \times \boldsymbol{r}

9.7: 長いソレノイド

  1. 長いソレノイド: 内部で B=μnIB=\mu n I, 外部で B=0B=0. 磁束 Φ=NBS(n=Nl)\Phi=N B S\left(n=\frac{N}{l}\right). インダクタンス L=L= Φ/I=μn2V\Phi / I=\mu n^2 V. 短いソレノイド :B∥=μnIΩ4π(Ω: B_{\|}=\frac{\mu n I \Omega}{4 \pi}(\Omega は 立体角).

9.8: 磁場を小型コイルや衝撃検流計で測定する

  1. 磁場を小型コイルや衝撃検流計で測定する： q=q= ∫VR dt=NSΔB/R\int \frac{V}{R} \mathrm{~d} t=N S \Delta B / R.

9.9: 静電場のエネルギー

  1. 静電場のエネルギー：

    U=k∑i<jqiqjrij=12∫ϕ(r)dq, dq=ρ(r)dVU=k \sum_{i<j} \frac{q_i q_j}{r_{i j}}=\frac{1}{2} \int \phi(\boldsymbol{r}) \mathrm{d} q, \mathrm{~d} q=\rho(\boldsymbol{r}) \mathrm{d} V

9.10: 一様に帯電した球面や円筒面の各部分の間に働く力

  1. 一様に帯電した球面や円筒面の各部分の間に働く力 : 帯電による力を静水圧による力に置き換える.

9.11: 全ての電荷

  1. 全ての電荷が距離 rr にある場合（例えば，不均一に帯 電した球やリングの中心） ϕϕ=kQ/r\phi \phi=k Q / r

9.12: 外部電荷

  1. 外部電荷によって引き起こされる正味の電荷（又は電 位）を求めるには, 電荷を「出現」させて問題を対称的 にし，重ね合わせの原理を用いる.

9.14: 導体

  1. 導体は電荷や電場を遮蔽する．例えば，中空の球体の 内部の電荷分布は外から見えない（あたかも QQ という 電荷を持った導電性の球があるように見える).

9.15: 静電容量

  1. 静電容量: C=εS/dC=\varepsilon S / d (平板), 4πεr4 \pi \varepsilon r (球), 2πεl(ln⁡R/r)−12 \pi \varepsilon l(\ln R / r)^{-1} (同軸円筒).

9.16: 双極子モーメント

  1. 双極子モーメント：

    pe=∑qiri=qd,pμ=IS\boldsymbol{p}_e=\sum q_i \boldsymbol{r}_i=q \boldsymbol{d}, \boldsymbol{p}_\mu=I \boldsymbol{S}

9.17: 双極子場

  1. 双極子場 : ϕ=kp⋅er/r2,E,B∝r−3\phi=k \boldsymbol{p} \cdot \boldsymbol{e}_r / r^2, E, B \propto r^{-3}

9.18: 双極子に働く力

  1. 双極子に働く力 : F=(pe⋅E)′,F=(pμ⋅B)′F=\left(\boldsymbol{p}_e \cdot \boldsymbol{E}\right)^{\prime}, F=\left(\boldsymbol{p}_\mu \cdot \boldsymbol{B}\right)^{\prime} [訳 者注 : ここの微分はむしろ grad⁡\operatorname{grad} である]. 2 つの双極 子間の相互作用 :F∝r−4: F \propto r^{-4}.

9.19: 磁気双極子としての点電荷

  1. 磁気双極子としての点電荷 : pμ∝Φ∝v⊥2/Bp_\mu \propto \Phi \propto v_{\perp}^2 / B は断熱 不変量 (Section 4: #22 参照).

9.20: 鏡像法

  1. 鏡像法 : 接地された（磁石の場合は超電導の）平面が鏡 の役割をする. 接地された（又は孤立した）球体の場 は, 球体の内部にある 1 つ（又は 2 つ）の架空の電荷 のつくる場として求められる. 平面導波管（金属板の 間のスリット）内の場は, 電磁平面波の重ね合わせと して求められる.

9.21: 一様（電）場中の球 (円柱) の分極

  1. 一様（電）場中の球 (円柱) の分極 : (+ρ(+\rho と −ρ-\rho に一 様に帯電した球 (円柱) の重ね合わせで， d∝Ed \propto E.

9.22: 渦電流

  1. 渦電流: 電流損失密度 ≈B2v2/ρ.1\approx B^2 v^2 / \rho .1 回の通過で与え られる運動量 : Fτ≈B2a3d/ρF \tau \approx B^2 a^3 d / \rho (ここで dd は厚さ, aa は大きさ).
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Formulas for IPhO 日本語版: Section 9

9: 電磁気学

9.1: Coulomb の法則

  1. F=kq1q2/r2,U=kq1q2/rF=k q_1 q_2 / r^2, U=k q_1 q_2 / r で, Kepler の法則が 使える (Section 12 参照).

9.2: Gauss の法則

  1. Gauss の法則 : ∮B⋅dS=0\oint \boldsymbol{B} \cdot \mathrm{d} \boldsymbol{S}=0,

    ∮εE⋅dS=Q,∮g⋅dS=−4πGM\oint \varepsilon \boldsymbol{E} \cdot \mathrm{d} \boldsymbol{S}=Q, \oint \boldsymbol{g} \cdot \mathrm{d} \boldsymbol{S}=-4 \pi G M

9.3: 循環定理

  1. 循環定理 :

    ∮E⋅dl=0(=Φ˙),∮B⋅dlμ=I,∮g⋅dl=0\oint \boldsymbol{E} \cdot \mathrm{d} \boldsymbol{l}=0(=\dot{\Phi}), \oint \frac{\boldsymbol{B} \cdot \mathrm{d} \boldsymbol{l}}{\mu}=I, \oint \boldsymbol{g} \cdot \mathrm{d} \boldsymbol{l}=0

9.4: 電流素片により生じる磁束密度

  1. 電流素片により生じる磁束密度 :

    dB=μI4πdl×err2.\mathrm{d} \boldsymbol{B}=\frac{\mu I}{4 \pi} \frac{\mathrm{d} \boldsymbol{l} \times \boldsymbol{e}_r}{r^2} .

    したがって電流 II が流れる円形回路の中心では B=μ0I2rB=\frac{\mu_0 I}{2 r}.

9.5: ローレンツ力

  1. F=e(E+v×B),F=I×Bl\boldsymbol{F}=e(\boldsymbol{E}+\boldsymbol{v} \times \boldsymbol{B}), \boldsymbol{F}=\boldsymbol{I} \times \boldsymbol{B} l.

9.6: Gauss の定理と循環定理より

  1. Gauss の定理と循環定理より：帯電した導線について E=σ2πε0rE=\frac{\sigma}{2 \pi \varepsilon_0 r}, 電流が流れる導線について B=μ0I2πrB=\frac{\mu_0 I}{2 \pi r}. 帯電した面について E=σ2ε0E=\frac{\sigma}{2 \varepsilon_0}, 電流が流れる面につい て B=μ0i2B=\frac{\mu_0 i}{2}. 一様に帯電した球殼（又は無限に長い円 筒）の内部で E=0E=0, 軸に沿って表面に電流が流れる 円筒の内部で B=0B=0. 密度 ρ\rho で一様に帯電, 又は一様 な電流 i\boldsymbol{i} が流れる, 球 (d=3)/(d=3) / 円柱 (d−2)/(d-2) / 平面 (d=1)(d=1) の内部で,

    E=ρεdr,B=1μdi×r\boldsymbol{E}=\frac{\rho}{\varepsilon d} \boldsymbol{r}, \boldsymbol{B}=\frac{1}{\mu d} \boldsymbol{i} \times \boldsymbol{r}

9.7: 長いソレノイド

  1. 長いソレノイド: 内部で B=μnIB=\mu n I, 外部で B=0B=0. 磁束 Φ=NBS(n=Nl)\Phi=N B S\left(n=\frac{N}{l}\right). インダクタンス L=L= Φ/I=μn2V\Phi / I=\mu n^2 V. 短いソレノイド :B∥=μnIΩ4π(Ω: B_{\|}=\frac{\mu n I \Omega}{4 \pi}(\Omega は 立体角).

9.8: 磁場を小型コイルや衝撃検流計で測定する

  1. 磁場を小型コイルや衝撃検流計で測定する： q=q= ∫VR dt=NSΔB/R\int \frac{V}{R} \mathrm{~d} t=N S \Delta B / R.

9.9: 静電場のエネルギー

  1. 静電場のエネルギー：

    U=k∑i<jqiqjrij=12∫ϕ(r)dq, dq=ρ(r)dVU=k \sum_{i<j} \frac{q_i q_j}{r_{i j}}=\frac{1}{2} \int \phi(\boldsymbol{r}) \mathrm{d} q, \mathrm{~d} q=\rho(\boldsymbol{r}) \mathrm{d} V

9.10: 一様に帯電した球面や円筒面の各部分の間に働く力

  1. 一様に帯電した球面や円筒面の各部分の間に働く力 : 帯電による力を静水圧による力に置き換える.

9.11: 全ての電荷

  1. 全ての電荷が距離 rr にある場合（例えば，不均一に帯 電した球やリングの中心） ϕϕ=kQ/r\phi \phi=k Q / r

9.12: 外部電荷

  1. 外部電荷によって引き起こされる正味の電荷（又は電 位）を求めるには, 電荷を「出現」させて問題を対称的 にし，重ね合わせの原理を用いる.

9.14: 導体

  1. 導体は電荷や電場を遮蔽する．例えば，中空の球体の 内部の電荷分布は外から見えない（あたかも QQ という 電荷を持った導電性の球があるように見える).

9.15: 静電容量

  1. 静電容量: C=εS/dC=\varepsilon S / d (平板), 4πεr4 \pi \varepsilon r (球), 2πεl(ln⁡R/r)−12 \pi \varepsilon l(\ln R / r)^{-1} (同軸円筒).

9.16: 双極子モーメント

  1. 双極子モーメント：

    pe=∑qiri=qd,pμ=IS\boldsymbol{p}_e=\sum q_i \boldsymbol{r}_i=q \boldsymbol{d}, \boldsymbol{p}_\mu=I \boldsymbol{S}

9.17: 双極子場

  1. 双極子場 : ϕ=kp⋅er/r2,E,B∝r−3\phi=k \boldsymbol{p} \cdot \boldsymbol{e}_r / r^2, E, B \propto r^{-3}

9.18: 双極子に働く力

  1. 双極子に働く力 : F=(pe⋅E)′,F=(pμ⋅B)′F=\left(\boldsymbol{p}_e \cdot \boldsymbol{E}\right)^{\prime}, F=\left(\boldsymbol{p}_\mu \cdot \boldsymbol{B}\right)^{\prime} [訳 者注 : ここの微分はむしろ grad⁡\operatorname{grad} である]. 2 つの双極 子間の相互作用 :F∝r−4: F \propto r^{-4}.

9.19: 磁気双極子としての点電荷

  1. 磁気双極子としての点電荷 : pμ∝Φ∝v⊥2/Bp_\mu \propto \Phi \propto v_{\perp}^2 / B は断熱 不変量 (Section 4: #22 参照).

9.20: 鏡像法

  1. 鏡像法 : 接地された（磁石の場合は超電導の）平面が鏡 の役割をする. 接地された（又は孤立した）球体の場 は, 球体の内部にある 1 つ（又は 2 つ）の架空の電荷 のつくる場として求められる. 平面導波管（金属板の 間のスリット）内の場は, 電磁平面波の重ね合わせと して求められる.

9.21: 一様（電）場中の球 (円柱) の分極

  1. 一様（電）場中の球 (円柱) の分極 : (+ρ(+\rho と −ρ-\rho に一 様に帯電した球 (円柱) の重ね合わせで， d∝Ed \propto E.

9.22: 渦電流

  1. 渦電流: 電流損失密度 ≈B2v2/ρ.1\approx B^2 v^2 / \rho .1 回の通過で与え られる運動量 : Fτ≈B2a3d/ρF \tau \approx B^2 a^3 d / \rho (ここで dd は厚さ, aa は大きさ).
+ diff --git a/academic/vocabulary/2023/02/2023-02-27.html b/academic/vocabulary/2023/02/2023-02-27.html index ea67e87e..f9fdc2d0 100644 --- a/academic/vocabulary/2023/02/2023-02-27.html +++ b/academic/vocabulary/2023/02/2023-02-27.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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2023-2-27: Vocabulary

This table of vocabularies are from "Sadlier Vocabulary Workshop-Level G (Unit 4)" with their corresponding textbook definitions and part of speeches (from some of them) made into a collection.

VocabularyDefinition
Atrophy(n.) the wasting away of a body organ or tissue; any progressive decline or failure; (v.) to waste away
BastionA fortified place, stronghold
ConcordA state of agreement, harmony, unanimity; a treaty, pact, covenant
Consummate(adj.) complete or perfect in the highest degree; (v.) to bring to a state of completion or perfection
Disarray(n.) disorder, confusion; (v.) to throw into disorder
ExigencyUrgency, pressure; urgent demand, pressing need; an emergency
FlotsamFloating debris; homeless, impoverished people
FreneticFrenzied, highly agitated
GleanTo gather bit by bit; to gather small quantities of grain left in a field by the reapers.
Grouse(n.) A type of game bird; a complaint; (v.) to complain, grumble
IncarcerateTo imprison, confine, jail
Incumbent(adj.) obligatory, required; (n.) one who holds a specific office at the time spoken of
JocularHumorous, jesting, jolly, joking
LudicrousRidiculous, laughable, absurd
MordantBiting or caustic in thought, manner, or style; sharply or bitterly harsh.
Nettle(n.) a prickly or stinging plant; (v.) to arouse displeasure, impatience, or anger; to vex or irritate severely
PecuniaryConsisting of or measured in money; of or related to money
PusillanimousContemptibly cowardly or mean-spirited
RecumbentIn a reclining position, lying down, in the posture of one sleeping or resting.
StratagemA scheme to outwit or deceive an opponent or to gain and end.

Reference

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2023-2-27: Vocabulary

This table of vocabularies are from "Sadlier Vocabulary Workshop-Level G (Unit 4)" with their corresponding textbook definitions and part of speeches (from some of them) made into a collection.

VocabularyDefinition
Atrophy(n.) the wasting away of a body organ or tissue; any progressive decline or failure; (v.) to waste away
BastionA fortified place, stronghold
ConcordA state of agreement, harmony, unanimity; a treaty, pact, covenant
Consummate(adj.) complete or perfect in the highest degree; (v.) to bring to a state of completion or perfection
Disarray(n.) disorder, confusion; (v.) to throw into disorder
ExigencyUrgency, pressure; urgent demand, pressing need; an emergency
FlotsamFloating debris; homeless, impoverished people
FreneticFrenzied, highly agitated
GleanTo gather bit by bit; to gather small quantities of grain left in a field by the reapers.
Grouse(n.) A type of game bird; a complaint; (v.) to complain, grumble
IncarcerateTo imprison, confine, jail
Incumbent(adj.) obligatory, required; (n.) one who holds a specific office at the time spoken of
JocularHumorous, jesting, jolly, joking
LudicrousRidiculous, laughable, absurd
MordantBiting or caustic in thought, manner, or style; sharply or bitterly harsh.
Nettle(n.) a prickly or stinging plant; (v.) to arouse displeasure, impatience, or anger; to vex or irritate severely
PecuniaryConsisting of or measured in money; of or related to money
PusillanimousContemptibly cowardly or mean-spirited
RecumbentIn a reclining position, lying down, in the posture of one sleeping or resting.
StratagemA scheme to outwit or deceive an opponent or to gain and end.

Reference

+ diff --git a/academic/vocabulary/index.html b/academic/vocabulary/index.html index 80a3f338..72be22a5 100644 --- a/academic/vocabulary/index.html +++ b/academic/vocabulary/index.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Welcome to My Vocabulary List!

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Welcome to My Vocabulary List!

+ diff --git a/application/markdown-it-katex/how-to-use.html b/application/markdown-it-katex/how-to-use.html index ddedefc4..39fac467 100644 --- a/application/markdown-it-katex/how-to-use.html +++ b/application/markdown-it-katex/how-to-use.html @@ -8,7 +8,7 @@ - + @@ -32,7 +32,7 @@
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@andatoshiki/markdown-it-katex

Add graceful KaTeX\KaTeX rendering to your Markdown like a charm with markdown-it plugin.

1: Installation

Before you start using this plugin, make sure you have already installed the default markdown-it parser; if not, please run the following command or refer to the official markdown-it documentation.

sh
$ npm install markdown-it --save
 
$ npm install markdown-it --save
-

First install package with your preferred package manager (npm, yarn, pnpm), or include javascript before the closing </body> for markdown-it-katex's core utils to be loaded for the static page.

sh
$ npm install -D @andatoshiki/markdown-it-katex
+

First install package with your preferred package manager (npm, yarn, pnpm), or include javascript before the closing </body> for markdown-it-katex's core utils to be loaded for the static page.

sh
$ npm install -D @andatoshiki/markdown-it-katex
 
$ npm install -D @andatoshiki/markdown-it-katex
sh
$ yarn add --dev @andatoshiki/markdown-it-katex
 
$ yarn add --dev @andatoshiki/markdown-it-katex
@@ -44,7 +44,7 @@
 
<!-- your other body contents ... -->
     <script src="https://unpkg.com/@andatoshiki/markdown-it-katex@0.0.3/markdown-it-katex.min.js"></script>
 </body>
-

Including KaTeX CSS is necessary in the way you are convenient with, either link the stylesheet from a third party CDN into the local HTML <head> tag or import it into a currently linked CSS stylesheets to enable styles for KaTeX globally as follows,

Or, you could clone or download the entire repository source of KaTeX and self load the fonts/styles/scripts locally, but if you prefer loading from third-party CDN with faster load speed when deployed to save your server resources, the following CDN links might be your choice, you can always switch to other platforms based on your need.

html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
+

Including KaTeX CSS is necessary in the way you are convenient with, either link the stylesheet from a third party CDN into the local HTML <head> tag or import it into a currently linked CSS stylesheets to enable styles for KaTeX globally as follows,

Or, you could clone or download the entire repository source of KaTeX and self load the fonts/styles/scripts locally, but if you prefer loading from third-party CDN with faster load speed when deployed to save your server resources, the following CDN links might be your choice, you can always switch to other platforms based on your need.

html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
 
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
html
<link rel="stylesheet" href="https://gcore.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
 
<link rel="stylesheet" href="https://gcore.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
@@ -60,7 +60,7 @@
 @import 'https://cdnjs.toshiki.dev/ajax/libs/KaTeX/0.16.0/katex.min.css';

If you are using the default markdown-it parser, I personally recommend that you use the GitHub markdown CSS (github-markdown-css) for styling your HTML output with a similar style replica of GitHub's markdown styling to your familiarity.

html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/github-markdown-css@5.2.0/github-markdown.min.css" />
 
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/github-markdown-css@5.2.0/github-markdown.min.css" />
-

This forked project maintained by Anda Toshiki comes with the update of KaTeX components with higher style version support (this documentation uses KaTeX version 16.0, without hassels), later versions may works, but no guarantees are given by the developers, if you are not obsessed with the latest released version, 16.0 may fits your need for loading KaTeX on a personal blog site or small educational sites; yet it should work fully functionally.

Warning

Since this project is a fork of the original markdown-it-katex project that hasn't been receiving any active updates of its code source for years, the latest katex style version supported is somewhere around ver. 0.9.0 which clearly is outdated and results in broken styles with overflowing and other potential bug presents.

2: Usage

RTo render equations, you need to include the markdown-it-katex plugin in the markdown-it components in your JavaScript or TypeScript file as follows,

js
var md = require('markdown-it')(),
+

This forked project maintained by Anda Toshiki comes with the update of KaTeX components with higher style version support (this documentation uses KaTeX version 16.0, without hassels), later versions may works, but no guarantees are given by the developers, if you are not obsessed with the latest released version, 16.0 may fits your need for loading KaTeX on a personal blog site or small educational sites; yet it should work fully functionally.

Warning

Since this project is a fork of the original markdown-it-katex project that hasn't been receiving any active updates of its code source for years, the latest katex style version supported is somewhere around ver. 0.9.0 which clearly is outdated and results in broken styles with overflowing and other potential bug presents.

2: Usage

RTo render equations, you need to include the markdown-it-katex plugin in the markdown-it components in your JavaScript or TypeScript file as follows,

js
var md = require('markdown-it')(),
     mk = require('andatoshiki/markdown-it-katex')
 
 md.use(mk)
@@ -113,8 +113,8 @@ M834 80h400000v40h-400000z">\frac {\partial^r} {\partial \omega^r} \left(\frac {y^{\omega}} {\omega}\right)
 = \left(\frac {y^{\omega}} {\omega}\right) \left\{(\log y)^r + \sum_{i=1}^r \frac {(-1)^ Ir \cdots (r-i+1) (\log y)^{ri}} {\omega^i} \right\}
 $$
-

the above block equation renders the LaTeX equation as a block with output as follows,

∂r∂ωr(yωω)=(yωω){(log⁡y)r+∑i=1r(−1)Ir⋯(r−i+1)(log⁡y)riωi}\frac {\partial^r} {\partial \omega^r} \left(\frac {y^{\omega}} {\omega}\right) = \left(\frac {y^{\omega}} {\omega}\right) \left\{(\log y)^r + \sum_{i=1}^r \frac {(-1)^ Ir \cdots (r-i+1) (\log y)^{ri}} {\omega^i} \right\}

5: Syntax

Math parsing in markdown is designed to comply with the "latex-in-markdown" conventions set by Pandoc,

Anything between two $ characters will be treated as TeX math. The opening $ must have a non-space character immediately to its right, while the closing $ must have a non-space character immediately to its left, and must not be followed immediately by a digit. Thus, $20,000 and $30,000 won’t parse as math. If for some reason you need to enclose text in literal $ characters, backslash-escape them and they won’t be treated as math delimiters.

6: Supported math syntax

KaTeX is a popular, open-source math typesetting library that is based on TeX and LaTeX. It is designed to be easy to use, and to provide high-quality mathematical typesetting for web applications, refer to the following pages of the document for the full list of function support in KaTeX.

Note

Due to the large number of equations rendered on the next following pages, it might takes time to entirely load the webpage, please be patient if the webpage seems to not respond; or it could be a result of slow network connection to correctly render all the equation that causes broken formulas, refresh the page to proceed.

- +

the above block equation renders the LaTeX equation as a block with output as follows,

∂r∂ωr(yωω)=(yωω){(log⁡y)r+∑i=1r(−1)Ir⋯(r−i+1)(log⁡y)riωi}\frac {\partial^r} {\partial \omega^r} \left(\frac {y^{\omega}} {\omega}\right) = \left(\frac {y^{\omega}} {\omega}\right) \left\{(\log y)^r + \sum_{i=1}^r \frac {(-1)^ Ir \cdots (r-i+1) (\log y)^{ri}} {\omega^i} \right\}

5: Syntax

Math parsing in markdown is designed to comply with the "latex-in-markdown" conventions set by Pandoc,

Anything between two $ characters will be treated as TeX math. The opening $ must have a non-space character immediately to its right, while the closing $ must have a non-space character immediately to its left, and must not be followed immediately by a digit. Thus, $20,000 and $30,000 won’t parse as math. If for some reason you need to enclose text in literal $ characters, backslash-escape them and they won’t be treated as math delimiters.

6: Supported math syntax

KaTeX is a popular, open-source math typesetting library that is based on TeX and LaTeX. It is designed to be easy to use, and to provide high-quality mathematical typesetting for web applications, refer to the following pages of the document for the full list of function support in KaTeX.

Note

Due to the large number of equations rendered on the next following pages, it might takes time to entirely load the webpage, please be patient if the webpage seems to not respond; or it could be a result of slow network connection to correctly render all the equation that causes broken formulas, refresh the page to proceed.

+ diff --git a/application/markdown-it-katex/support-function.html b/application/markdown-it-katex/support-function.html index 57cff197..3382ea2d 100644 --- a/application/markdown-it-katex/support-function.html +++ b/application/markdown-it-katex/support-function.html @@ -8,7 +8,7 @@ - + @@ -328,8 +328,8 @@ M40 281 V448H0V74H40V241H400000v40z">​ \xmapsto{abc}

|=abc\xlongequal{abc} \xlongequal{abc}

Extensible arrows all can take an optional argument in the same manner, as \xrightarrow[under]{over}.

11: Style, Color, Size, and Font

Class Assignment

Color

F=ma\color{blue} F=ma \color{blue} F=ma

Note that KaTeX \color acts like a switch. This aligns with LaTeX and differs from MathJax. Other KaTeX color functions expect the content to be a function argument:

For color definition, KaTeX color functions will accept the standard HTML predefined color names. They will also accept an RGB argument in CSS hexa­decimal style. The "#" is optional before a six-digit specification.

Font

Ab0\mathrm{Ab0} \mathrm{Ab0}Ab0\mathbf{Ab0} \mathbf{Ab0}Ab\mathit{Ab} \mathit{Ab}
Ab0\mathnormal{Ab0} \mathnormal{Ab0}Ab0\textbf{Ab0} \textbf{Ab0}Ab\textit{Ab} \textit{Ab}
Ab0\textrm{Ab0} \textrm{Ab0}Ab0\bf Ab0 \bf Ab0Ab\it Ab \it Ab
Ab0\rm Ab0 \rm Ab0Ab0\bold{Ab0} \bold{Ab0}AB\Bbb{AB} \Bbb{AB}
Ab0\textnormal{Ab0} \textnormal{Ab0}Ab\boldsymbol{Ab} \boldsymbol{Ab}AB\mathbb{AB} \mathbb{AB}
Ab0\text{Ab0} \text{Ab0}Ab\bm{Ab} \bm{Ab}Ab0\frak{Ab0} \frak{Ab0}
Ab0\mathsf{Ab0} \mathsf{Ab0}Ab0\mathtt{Ab0} \mathtt{Ab0}Ab0\mathfrak{Ab0} \mathfrak{Ab0}
Ab0\textsf{Ab0} \textsf{Ab0}Ab0\texttt{Ab0} \texttt{Ab0}AB0\mathcal{AB0} \mathcal{AB0}
Ab0\sf Ab0 \sf Ab0Ab0\tt Ab0 \tt Ab0AB\mathscr{AB} \mathscr{AB}

One can stack font family, font weight, and font shape by using the \textXX versions of the font functions. So \textsf{\textbf{H}} will produce H\textsf{\textbf{H}}. The other versions do not stack, e.g., \mathsf{\mathbf{H}} will produce H\mathsf{\mathbf{H}}.

In cases where KaTeX fonts do not have a bold glyph, \pmb can simulate one. For example, \pmb{\mu} renders as : μ\pmb{\mu}

Size

AB\Huge AB \Huge ABAB\normalsize AB \normalsize AB
AB\huge AB \huge ABAB\small AB \small AB
AB\LARGE AB \LARGE ABAB\footnotesize AB \footnotesize AB
AB\Large AB \Large ABAB\scriptsize AB \scriptsize AB
AB\large AB \large ABAB\tiny AB \tiny AB

Style

|∑i=1n\displaystyle\sum_{i=1}^n \displaystyle\sum_{i=1}^n |∑i=1n\textstyle\sum_{i=1}^n \textstyle\sum_{i=1}^n |x\scriptstyle x \scriptstyle x         (The size of a first sub/superscript) |x\scriptscriptstyle x \scriptscriptstyle x (The size of subsequent sub/superscripts) |lim⁡x\lim\limits_x \lim\limits_x |lim⁡x\lim\nolimits_x \lim\nolimits_x |x^2\verb!x^2! \verb!x^2!

\text{…} will accept nested $…$ fragments and render them in math mode.

12: Symbols and Punctuation

% comment…\dots \dotsKaTeX\KaTeX \KaTeX
%\% \%⋯\cdots \cdotsLaTeX\LaTeX \LaTeX
#\# \#⋱\ddots \ddotsTeX\TeX \TeX
&\& \&…\ldots \ldots∇\nabla \nabla
_\_ \_⋮\vdots \vdots∞\infty \infty
_\text{\textunderscore} \text{\textunderscore}⋯\dotsb \dotsb∞\infin \infin
–\text{--} \text{--}…\dotsc \dotsc✓\checkmark \checkmark
–\text{\textendash} \text{\textendash} ⁣⋯\dotsi \dotsi†\dag \dag
—\text{---} \text{---}⋯\dotsm \dotsm†\dagger \dagger
—\text{\textemdash} \text{\textemdash}…\dotso \dotso†\text{\textdagger} \text{\textdagger}
~\text{\textasciitilde} \text{\textasciitilde}⋅\sdot \sdot‡\ddag \ddag
‘` `…\mathellipsis \mathellipsis‡\ddagger \ddagger
‘\text{\textquoteleft} text{\textquoteleft}…\text{\textellipsis} \text{\textellipsis}‡\text{\textdaggerdbl} \text{\textdaggerdbl}
‘\lq \lq□\Box \Box‡\Dagger \Dagger
’\text{\textquoteright} \text{\textquoteright}□\square \square∠\angle \angle
′\rq \rq■\blacksquare \blacksquare∡\measuredangle \measuredangle
“\text{\textquotedblleft} \text{\textquotedblleft}△\triangle \triangle∢\sphericalangle \sphericalangle
"" "▽\triangledown \triangledown⊤\top \top
”\text{\textquotedblright} \text{\textquotedblright}◃\triangleleft \triangleleft⊥\bot \bot
 ⁣:\colon \colon▹\triangleright \triangleright$\$ \$
‵\backprime \backprime▽\bigtriangledown \bigtriangledown$\text{\textdollar} \text{\textdollar}
′\prime \prime△\bigtriangleup \bigtriangleup£\pounds \pounds
<\text{\textless} \text{\textless}▲\blacktriangle \blacktriangle£\mathsterling \mathsterling
>\text{\textgreater} \text{\textgreater}▼\blacktriangledown \blacktriangledown£\text{\textsterling} \text{\textsterling}
|\text{\textbar} \text{\textbar}◀\blacktriangleleft \blacktriangleleft¥\yen \yen
∥\text{\textbardbl} \text{\textbardbl}▶\blacktriangleright \blacktriangleright√\surd \surd
{\text{\textbraceleft} \text{\textbraceleft}⋄\diamond \diamond°\degree \degree
}\text{\textbraceright} \text{\textbraceright}◊\Diamond \Diamond°\text{\textdegree} \text{\textdegree}
\text{\P} \text{\P}◊\lozenge \lozenge℧\mho \mho
§\text{\S} \text{\S}⧫\blacklozenge \blacklozenge╲\diagdown \diagdown
§\text{\sect} \text{\sect}⋆\star \star╱\diagup \diagup
©\copyright \copyright★\bigstar \bigstar♭\flat \flat
®\circledR \circledR♣\clubsuit \clubsuit♮\natural \natural
®\text{\textregistered} \text{\textregistered}♣\clubs \clubs♯\sharp \sharp
Ⓢ\circledS \circledS♢\diamondsuit \diamondsuit♡\heartsuit \heartsuit
a◯\text{\textcircled a} \text{\textcircled a}♢\diamonds \diamonds♡\hearts \hearts
✠\maltese \maltese♠\spadesuit \spadesuit♠\spades \spades

Direct Input: £¥∇∞⋅∠∡∢♠♡♢♣♭♮♯✓…⋮⋯⋱!£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ ! ‼

13: Units

In KaTeX, units are proportioned as they are in TeX. KaTeX units are different than CSS units.

KaTeX UnitValueKaTeX UnitValue
emCSS embp1/72​ inch × F × G
exCSS expc12 KaTeX pt
mu1/18 CSS emdd1238/1157​ KaTeX pt
pt1/72.27 inch × F × Gcc14856/1157 KaTeX pt
mm1 mm × F × Gnd685/642 KaTeX pt
cm1 cm × F × Gnc1370/107​ KaTeX pt
in1 inch × F × Gsp1/65536 KaTeX pt

where:

The effect of style and size:

Unittextstylescriptscripthuge
em or ex\rule{1em}{1em}\scriptscriptstyle\rule{1em}{1em}\huge\rule{1em}{1em}
mu\rule{18mu}{18mu}\scriptscriptstyle\rule{18mu}{18mu}\huge\rule{18mu}{18mu}
others\rule{10pt}{10pt}\scriptscriptstyle\rule{10pt}{10pt}\huge\rule{10pt}{10pt}
- +M0 50 h400000 v40H0z m0 194h40000v40H0z"> \xlongequal{abc}

Extensible arrows all can take an optional argument in the same manner, as \xrightarrow[under]{over}.

11: Style, Color, Size, and Font

Class Assignment

Color

F=ma\color{blue} F=ma \color{blue} F=ma

Note that KaTeX \color acts like a switch. This aligns with LaTeX and differs from MathJax. Other KaTeX color functions expect the content to be a function argument:

For color definition, KaTeX color functions will accept the standard HTML predefined color names. They will also accept an RGB argument in CSS hexa­decimal style. The "#" is optional before a six-digit specification.

Font

Ab0\mathrm{Ab0} \mathrm{Ab0}Ab0\mathbf{Ab0} \mathbf{Ab0}Ab\mathit{Ab} \mathit{Ab}
Ab0\mathnormal{Ab0} \mathnormal{Ab0}Ab0\textbf{Ab0} \textbf{Ab0}Ab\textit{Ab} \textit{Ab}
Ab0\textrm{Ab0} \textrm{Ab0}Ab0\bf Ab0 \bf Ab0Ab\it Ab \it Ab
Ab0\rm Ab0 \rm Ab0Ab0\bold{Ab0} \bold{Ab0}AB\Bbb{AB} \Bbb{AB}
Ab0\textnormal{Ab0} \textnormal{Ab0}Ab\boldsymbol{Ab} \boldsymbol{Ab}AB\mathbb{AB} \mathbb{AB}
Ab0\text{Ab0} \text{Ab0}Ab\bm{Ab} \bm{Ab}Ab0\frak{Ab0} \frak{Ab0}
Ab0\mathsf{Ab0} \mathsf{Ab0}Ab0\mathtt{Ab0} \mathtt{Ab0}Ab0\mathfrak{Ab0} \mathfrak{Ab0}
Ab0\textsf{Ab0} \textsf{Ab0}Ab0\texttt{Ab0} \texttt{Ab0}AB0\mathcal{AB0} \mathcal{AB0}
Ab0\sf Ab0 \sf Ab0Ab0\tt Ab0 \tt Ab0AB\mathscr{AB} \mathscr{AB}

One can stack font family, font weight, and font shape by using the \textXX versions of the font functions. So \textsf{\textbf{H}} will produce H\textsf{\textbf{H}}. The other versions do not stack, e.g., \mathsf{\mathbf{H}} will produce H\mathsf{\mathbf{H}}.

In cases where KaTeX fonts do not have a bold glyph, \pmb can simulate one. For example, \pmb{\mu} renders as : μ\pmb{\mu}

Size

AB\Huge AB \Huge ABAB\normalsize AB \normalsize AB
AB\huge AB \huge ABAB\small AB \small AB
AB\LARGE AB \LARGE ABAB\footnotesize AB \footnotesize AB
AB\Large AB \Large ABAB\scriptsize AB \scriptsize AB
AB\large AB \large ABAB\tiny AB \tiny AB

Style

|∑i=1n\displaystyle\sum_{i=1}^n \displaystyle\sum_{i=1}^n |∑i=1n\textstyle\sum_{i=1}^n \textstyle\sum_{i=1}^n |x\scriptstyle x \scriptstyle x         (The size of a first sub/superscript) |x\scriptscriptstyle x \scriptscriptstyle x (The size of subsequent sub/superscripts) |lim⁡x\lim\limits_x \lim\limits_x |lim⁡x\lim\nolimits_x \lim\nolimits_x |x^2\verb!x^2! \verb!x^2!

\text{…} will accept nested $…$ fragments and render them in math mode.

12: Symbols and Punctuation

% comment…\dots \dotsKaTeX\KaTeX \KaTeX
%\% \%⋯\cdots \cdotsLaTeX\LaTeX \LaTeX
#\# \#⋱\ddots \ddotsTeX\TeX \TeX
&\& \&…\ldots \ldots∇\nabla \nabla
_\_ \_⋮\vdots \vdots∞\infty \infty
_\text{\textunderscore} \text{\textunderscore}⋯\dotsb \dotsb∞\infin \infin
–\text{--} \text{--}…\dotsc \dotsc✓\checkmark \checkmark
–\text{\textendash} \text{\textendash} ⁣⋯\dotsi \dotsi†\dag \dag
—\text{---} \text{---}⋯\dotsm \dotsm†\dagger \dagger
—\text{\textemdash} \text{\textemdash}…\dotso \dotso†\text{\textdagger} \text{\textdagger}
~\text{\textasciitilde} \text{\textasciitilde}⋅\sdot \sdot‡\ddag \ddag
‘` `…\mathellipsis \mathellipsis‡\ddagger \ddagger
‘\text{\textquoteleft} text{\textquoteleft}…\text{\textellipsis} \text{\textellipsis}‡\text{\textdaggerdbl} \text{\textdaggerdbl}
‘\lq \lq□\Box \Box‡\Dagger \Dagger
’\text{\textquoteright} \text{\textquoteright}□\square \square∠\angle \angle
′\rq \rq■\blacksquare \blacksquare∡\measuredangle \measuredangle
“\text{\textquotedblleft} \text{\textquotedblleft}△\triangle \triangle∢\sphericalangle \sphericalangle
"" "▽\triangledown \triangledown⊤\top \top
”\text{\textquotedblright} \text{\textquotedblright}◃\triangleleft \triangleleft⊥\bot \bot
 ⁣:\colon \colon▹\triangleright \triangleright$\$ \$
‵\backprime \backprime▽\bigtriangledown \bigtriangledown$\text{\textdollar} \text{\textdollar}
′\prime \prime△\bigtriangleup \bigtriangleup£\pounds \pounds
<\text{\textless} \text{\textless}▲\blacktriangle \blacktriangle£\mathsterling \mathsterling
>\text{\textgreater} \text{\textgreater}▼\blacktriangledown \blacktriangledown£\text{\textsterling} \text{\textsterling}
|\text{\textbar} \text{\textbar}◀\blacktriangleleft \blacktriangleleft¥\yen \yen
∥\text{\textbardbl} \text{\textbardbl}▶\blacktriangleright \blacktriangleright√\surd \surd
{\text{\textbraceleft} \text{\textbraceleft}⋄\diamond \diamond°\degree \degree
}\text{\textbraceright} \text{\textbraceright}◊\Diamond \Diamond°\text{\textdegree} \text{\textdegree}
\text{\P} \text{\P}◊\lozenge \lozenge℧\mho \mho
§\text{\S} \text{\S}⧫\blacklozenge \blacklozenge╲\diagdown \diagdown
§\text{\sect} \text{\sect}⋆\star \star╱\diagup \diagup
©\copyright \copyright★\bigstar \bigstar♭\flat \flat
®\circledR \circledR♣\clubsuit \clubsuit♮\natural \natural
®\text{\textregistered} \text{\textregistered}♣\clubs \clubs♯\sharp \sharp
Ⓢ\circledS \circledS♢\diamondsuit \diamondsuit♡\heartsuit \heartsuit
a◯\text{\textcircled a} \text{\textcircled a}♢\diamonds \diamonds♡\hearts \hearts
✠\maltese \maltese♠\spadesuit \spadesuit♠\spades \spades

Direct Input: £¥∇∞⋅∠∡∢♠♡♢♣♭♮♯✓…⋮⋯⋱!£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ ! ‼

13: Units

In KaTeX, units are proportioned as they are in TeX. KaTeX units are different than CSS units.

KaTeX UnitValueKaTeX UnitValue
emCSS embp1/72​ inch × F × G
exCSS expc12 KaTeX pt
mu1/18 CSS emdd1238/1157​ KaTeX pt
pt1/72.27 inch × F × Gcc14856/1157 KaTeX pt
mm1 mm × F × Gnd685/642 KaTeX pt
cm1 cm × F × Gnc1370/107​ KaTeX pt
in1 inch × F × Gsp1/65536 KaTeX pt

where:

The effect of style and size:

Unittextstylescriptscripthuge
em or ex\rule{1em}{1em}\scriptscriptstyle\rule{1em}{1em}\huge\rule{1em}{1em}
mu\rule{18mu}{18mu}\scriptscriptstyle\rule{18mu}{18mu}\huge\rule{18mu}{18mu}
others\rule{10pt}{10pt}\scriptscriptstyle\rule{10pt}{10pt}\huge\rule{10pt}{10pt}
+ diff --git a/application/markdown-it-katex/support-table.html b/application/markdown-it-katex/support-table.html index 3dfca2c0..f6e539b9 100644 --- a/application/markdown-it-katex/support-table.html +++ b/application/markdown-it-katex/support-table.html @@ -8,7 +8,7 @@ - + @@ -302,8 +302,8 @@ c-68-40-115.7-95.7-143-167h-22c-15.3 0-23 .3-23 1 0 1.3 5.3 13.7 16 37 18 35.3 41.3 69 70 101l7 8h-125l-9-7c-50.7-39.3-85-86-103-140h-46c0 4.7 6.3 18.7 19 42 18 35.3 40 67.3 66 96l9 9H0v40h399716l-9 9c-26 28.7-48 60.7-66 96-12.7 23.333 -19 37.333-19 42h46c18-54 52.3-100.7 103-140l9-7h125l-7 8c-28.7 32-52 65.7-70 - 101-10.7 23.333-16 35.7-16 37 0 .7 7.7 1 23 1h22c27.3-71.3 75-127 143-167z">\xtwoheadrightarrow{abc}

YZ

Symbol/FunctionRenderedSource or Comment
\yen¥\yen
\ZZ\Z
\ZetaZ\Zeta
\zetaζ\zeta
- + 101-10.7 23.333-16 35.7-16 37 0 .7 7.7 1 23 1h22c27.3-71.3 75-127 143-167z">\xtwoheadrightarrow{abc}

YZ

Symbol/FunctionRenderedSource or Comment
\yen¥\yen
\ZZ\Z
\ZetaZ\Zeta
\zetaζ\zeta
+ diff --git a/assets/academic_chemistry_index.md.fa53861e.js b/assets/academic_chemistry_index.md.7e5c2af2.js similarity index 88% rename from assets/academic_chemistry_index.md.fa53861e.js rename to assets/academic_chemistry_index.md.7e5c2af2.js index 533b6c63..e8028ff8 100644 --- a/assets/academic_chemistry_index.md.fa53861e.js +++ b/assets/academic_chemistry_index.md.7e5c2af2.js @@ -1 +1 @@ -import{_ as t,c as a,o as c,a as e,b as o}from"./app.b4df1b52.js";const x=JSON.parse('{"title":"Welcome to Chemistry","description":"","frontmatter":{},"headers":[],"relativePath":"academic/chemistry/index.md","lastUpdated":1679649941000}'),s={name:"academic/chemistry/index.md"},r=e("h1",{id:"welcome-to-chemistry",tabindex:"-1"},[o("Welcome to Chemistry "),e("a",{class:"header-anchor",href:"#welcome-to-chemistry","aria-hidden":"true"},"#")],-1),i=[r];function d(n,m,h,_,l,p){return c(),a("div",null,i)}const u=t(s,[["render",d]]);export{x as __pageData,u as default}; +import{_ as t,c as a,o as c,a as e,b as o}from"./app.b4df1b52.js";const x=JSON.parse('{"title":"Welcome to Chemistry","description":"","frontmatter":{},"headers":[],"relativePath":"academic/chemistry/index.md","lastUpdated":1679745767000}'),s={name:"academic/chemistry/index.md"},r=e("h1",{id:"welcome-to-chemistry",tabindex:"-1"},[o("Welcome to Chemistry "),e("a",{class:"header-anchor",href:"#welcome-to-chemistry","aria-hidden":"true"},"#")],-1),i=[r];function d(n,m,h,_,l,p){return c(),a("div",null,i)}const u=t(s,[["render",d]]);export{x as __pageData,u as default}; 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12-5: Reaction Mechanism

12-5-1: Learning Objectives

Learning Objectives

One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system, such as the rate of change in the concentration of reactants or products with time, to discover the sequence of events that occur at the molecular level during a reaction. This molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products. The stepwise changes are collectively called the reaction mechanism.

In an internal combustion engine, for example, isooctane reacts with oxygen to give carbon dioxide and water:

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12-5: Reaction Mechanism

12-5-1: Learning Objectives

Learning Objectives

One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system, such as the rate of change in the concentration of reactants or products with time, to discover the sequence of events that occur at the molecular level during a reaction. This molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products. The stepwise changes are collectively called the reaction mechanism.

In an internal combustion engine, for example, isooctane reacts with oxygen to give carbon dioxide and water:

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It is more likely that a complex series of reactions takes place in a stepwise fashion. Each individual reaction, which is called an elementary reaction, involves one, two, or (rarely) three atoms, molecules, or ions. The overall sequence of elementary reactions is the mechanism of the reaction. The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.",-1),p=s("p",null,"The overall sequence of elementary reactions is the mechanism of the reaction.",-1),h=s("h2",{id:"_12-5-2-molecularity-and-the-rate-determining-step",tabindex:"-1"},[a("12-5-2: Molecularity and the Rate-Determining Step "),s("a",{class:"header-anchor",href:"#_12-5-2-molecularity-and-the-rate-determining-step","aria-hidden":"true"},"#")],-1),o=s("p",null,"To demonstrate how the analysis of elementary reactions helps us determine the overall reaction mechanism, we will examine the much simpler reaction of carbon monoxide with nitrogen 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It is more likely that a complex series of reactions takes place in a stepwise fashion. Each individual reaction, which is called an elementary reaction, involves one, two, or (rarely) three atoms, molecules, or ions. The overall sequence of elementary reactions is the mechanism of the reaction. The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.",-1),p=s("p",null,"The overall sequence of elementary reactions is the mechanism of the reaction.",-1),h=s("h2",{id:"_12-5-2-molecularity-and-the-rate-determining-step",tabindex:"-1"},[a("12-5-2: Molecularity and the Rate-Determining Step "),s("a",{class:"header-anchor",href:"#_12-5-2-molecularity-and-the-rate-determining-step","aria-hidden":"true"},"#")],-1),o=s("p",null,"To demonstrate how the analysis of elementary reactions helps us determine the overall reaction mechanism, we will examine the much simpler reaction of carbon monoxide with nitrogen 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reaction represented above is found to be second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord 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Solution

',2),d=a("p",null,[s("To solve this problem, let's first write out the rate law for the reaction. According to the text, the reaction is second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y")])])]),s(", so the rate law is rate "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",null,"="),a("mi",null,"k"),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("msup",null,[a("mo",{stretchy:"false"},"]"),a("mn",null,"2")]),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"=k[\\mathrm{X}]^2[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.3669em"}}),a("span",{class:"mrel"},"="),a("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),a("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},[a("span",{class:"mclose"},"]"),a("span",{class:"msupsub"},[a("span",{class:"vlist-t"},[a("span",{class:"vlist-r"},[a("span",{class:"vlist",style:{height:"0.8141em"}},[a("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[a("span",{class:"pstrut",style:{height:"2.7em"}}),a("span",{class:"sizing reset-size6 size3 mtight"},[a("span",{class:"mord mtight"},"2")])])])])])])]),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])])],-1),g=a("p",null,[s("Now, let's think about how the rate changes when "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is halved and "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled. Since "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is raised to the second power in the rate law, halving "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" decreases the reaction rate by a factor of 4 . Similarly, since "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is raised to the first power, doubling "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" increases the reaction rate by a factor of 2 . Combined, these changes result in the reaction rate decreasing by a factor of 2 overall. So, when "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is halved and "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled, the rate of the reaction decreases by a factor of 2 .")],-1),u=[r,i,c,o,h,p,d,g];function x(w,y,k,f,b,v){return l(),e("div",null,u)}const X=t(m,[["render",x]]);export{_ as __pageData,X as default}; +import{_ as t,c as e,o as l,a,b as s,d as n}from"./app.b4df1b52.js";const _=JSON.parse('{"title":"Problem 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reaction represented above is found to be second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord 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"),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled?")],-1),p=n('

Solution

',2),d=a("p",null,[s("To solve this problem, let's first write out the rate law for the reaction. According to the text, the reaction is second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y")])])]),s(", so the rate law is rate "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",null,"="),a("mi",null,"k"),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("msup",null,[a("mo",{stretchy:"false"},"]"),a("mn",null,"2")]),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"=k[\\mathrm{X}]^2[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.3669em"}}),a("span",{class:"mrel"},"="),a("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),a("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},[a("span",{class:"mclose"},"]"),a("span",{class:"msupsub"},[a("span",{class:"vlist-t"},[a("span",{class:"vlist-r"},[a("span",{class:"vlist",style:{height:"0.8141em"}},[a("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[a("span",{class:"pstrut",style:{height:"2.7em"}}),a("span",{class:"sizing reset-size6 size3 mtight"},[a("span",{class:"mord mtight"},"2")])])])])])])]),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])])],-1),g=a("p",null,[s("Now, let's think about how the rate changes when "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is halved and "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled. Since "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is raised to the second power in the rate law, halving "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" decreases the reaction rate by a factor of 4 . Similarly, since "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is raised to the first power, doubling "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" increases the reaction rate by a factor of 2 . Combined, these changes result in the reaction rate decreasing by a factor of 2 overall. So, when "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is halved and "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled, the rate of the reaction decreases by a factor of 2 .")],-1),u=[r,i,c,o,h,p,d,g];function x(w,y,k,f,b,v){return l(),e("div",null,u)}const X=t(m,[["render",x]]);export{_ as __pageData,X as default}; diff --git a/assets/academic_chemistry_problems_03-02-3.md.c0d95fdc.lean.js b/assets/academic_chemistry_problems_03-02-3.md.19495002.lean.js similarity index 99% rename from assets/academic_chemistry_problems_03-02-3.md.c0d95fdc.lean.js rename to assets/academic_chemistry_problems_03-02-3.md.19495002.lean.js index a14eb86b..648f1e59 100644 --- a/assets/academic_chemistry_problems_03-02-3.md.c0d95fdc.lean.js +++ b/assets/academic_chemistry_problems_03-02-3.md.19495002.lean.js @@ -1 +1 @@ -import{_ as t,c as e,o as l,a,b as s,d as n}from"./app.b4df1b52.js";const _=JSON.parse('{"title":"Problem 03-02-3","description":"","frontmatter":{},"headers":[{"level":2,"title":"Question","slug":"question","link":"#question","children":[]},{"level":2,"title":"Solution","slug":"solution","link":"#solution","children":[]}],"relativePath":"academic/chemistry/problems/03-02-3.md","lastUpdated":1679649941000}'),m={name:"academic/chemistry/problems/03-02-3.md"},r=a("h1",{id:"problem-03-02-3",tabindex:"-1"},[s("Problem 03-02-3 "),a("a",{class:"header-anchor",href:"#problem-03-02-3","aria-hidden":"true"},"#")],-1),i=a("h2",{id:"question",tabindex:"-1"},[s("Question 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reaction represented above is found to be second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord 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According to the text, the reaction is second order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"X")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{X}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm"},"X")])])]),s(" and first order with respect to "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mi",{mathvariant:"normal"},"Y")]),a("annotation",{encoding:"application/x-tex"},"\\mathrm{Y}")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.6833em"}}),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y")])])]),s(", so the rate law is rate "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",null,"="),a("mi",null,"k"),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("msup",null,[a("mo",{stretchy:"false"},"]"),a("mn",null,"2")]),a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"=k[\\mathrm{X}]^2[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"0.3669em"}}),a("span",{class:"mrel"},"="),a("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),a("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},[a("span",{class:"mclose"},"]"),a("span",{class:"msupsub"},[a("span",{class:"vlist-t"},[a("span",{class:"vlist-r"},[a("span",{class:"vlist",style:{height:"0.8141em"}},[a("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[a("span",{class:"pstrut",style:{height:"2.7em"}}),a("span",{class:"sizing reset-size6 size3 mtight"},[a("span",{class:"mord mtight"},"2")])])])])])])]),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])])],-1),g=a("p",null,[s("Now, let's think about how the rate changes when "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is halved and "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"Y"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{Y}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm",style:{"margin-right":"0.025em"}},"Y"),a("span",{class:"mclose"},"]")])])]),s(" is doubled. Since "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" is raised to the second power in the rate law, halving "),a("span",{class:"katex"},[a("span",{class:"katex-mathml"},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("semantics",null,[a("mrow",null,[a("mo",{stretchy:"false"},"["),a("mi",{mathvariant:"normal"},"X"),a("mo",{stretchy:"false"},"]")]),a("annotation",{encoding:"application/x-tex"},"[\\mathrm{X}]")])])]),a("span",{class:"katex-html","aria-hidden":"true"},[a("span",{class:"base"},[a("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),a("span",{class:"mopen"},"["),a("span",{class:"mord mathrm"},"X"),a("span",{class:"mclose"},"]")])])]),s(" decreases the reaction rate by a factor of 4 . 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Patterns of Organization and Methods of Development

Patterns of organization can help your readers follow the ideas within your essay and your paragraphs, but they can also work as methods of development to help you recognize and further develop ideas and relationships in your writing. Here are some strategies that can help you with both organization and development in your essays.

Major Patterns of Organization

A fruit pie.

Read the following sentences:

How did it feel to read the above list? A bit confusing, I would guess. That’s because the steps for making a pie were not well organized, and the steps don’t include enough detail for us to know exactly what we should do. (Like what are the dry and liquid ingredients?) We all know that starting instructions from the beginning and giving each detailed step in the order it should happen is vital to having a good outcome, in this case a yummy pie! But it’s not always so simple to know how to organize or develop ideas, and sometimes there’s more than one way, which complicates things even further.

First, let’s take a look at a couple of ways to think about organization.

General to Specific or Specific to General

It might be useful to think about organizing your topic like a triangle:

Two triangles. The first is an inverted pyramid for General to Specific, the second is a pyramid for Specific to General.

The first triangle represents starting with the most general, big picture information first, moving then to more detailed and often more personal information later in the paper. The second triangle represents an organizational structure that starts with the specific, small scale information first and then moves to the more global, big picture stuff.

For example, if your topic is traffic in Vancouver, British Columbia, an essay that uses the general-to-specific organizational structure might begin this way:

Many people consider Vancouver, British Columbia, to be a relaxed place to live. They would be shocked to know how bad the traffic is traveling major arteries into the city and even driving around the city itself.

An essay that uses the specific-to-general structure might start like this:

Transit is crowded, parking is expensive, and vehicles stop and go through the main streets of the city of Vancouver, British Columbia, and that is just once travelers brave the crowded arteries to enter the city; Vancouver’s traffic problem does not lend itself to the relaxed atmosphere many believe the city to have.

What’s the difference between these two introductions? And how might they appeal to the intended audience for this essay in different ways? The first introduction is looking at the big picture of the problem and mentions pollution’s impact on all citizens in Portland, while the second introduction focuses on one specific family. The first helps readers see how vast the problem really is, and the second helps connect readers to a real family, making an emotional appeal from the very beginning. Neither introduction is necessarily better. You’ll choose one over the other based on the kind of tone you’d like to create and how you’d like to affect your audience. It’s completely up to you to make this decision.

Does the Triangle Mean the Essay Keeps Getting More Specific or More Broad until the Very End?

The triangle is kind of a general guide, meaning you’re allowed to move around within it all you want. For example, it’s possible that each of your paragraphs will be its own triangle, starting with the general or specific and moving out or in. However, if you begin very broadly, it might be effective to end your essay in a more specific, personal way. And if you begin with a personal story, consider ending your essay by touching on the global impact and importance of your topic.

Are There Other Ways to Think about Organizing My Ideas?

Yes! Rather than thinking about which of your ideas are most specific or personal or which are more broad or universal, you might consider one of the following ways of organizing your ideas:

The section on Methods of Development, below, offers more detail about some of these organizational patterns, along with some others.

Choose one of the following topics, and practice writing a few opening sentences like we did above, once using the general-to-specific format and once using the specific-to-general. Which do you like better? What audience would be attracted to which one? Share with peers to see how others tackled this challenge. How would you rewrite their sentences? Why? Discuss your changes and listen to how your peers have revised your sentences. Taking in other people’s ideas will help you see new ways to approach your own writing and thinking.
Topics:

Methods of Development

The methods of development covered here are best used as ways to look at what’s already happening in your draft and to consider how you might emphasize or expand on any existing patterns. You might already be familiar with some of these patterns because teachers will sometimes assign them as the purpose for writing an essay. For example, you might have been asked to write a cause-and-effect essay or a comparison-and-contrast essay.

It’s important to emphasize here that patterns of organization or methods of developing content usually happen naturally as a consequence of the way the writer engages with and organizes information while writing. That is to say, most writers don’t sit down and say, “I think I’ll write a cause-and-effect essay today.” Instead, a writer might be more likely to be interested in a topic, say, the state of drinking water in the local community, and as the writer begins to explore the topic, certain cause-and-effect relationships between environmental pollutants and the community water supply may begin to emerge.

So if these patterns just occur naturally in writing, what’s the use in knowing about them? Well, sometimes you might be revising a draft and notice that some of your paragraphs are a bit underdeveloped. Maybe they lack a clear topic, or maybe they lack support. In either case, you can look to these common methods of development to find ways to sharpen those vague topics or to add support where needed. Do you have a clear cause statement somewhere but you haven’t explored the effects? Are you lacking detail somewhere where a narrative story or historical chronology can help build reader interest and add support? Are you struggling to define an idea that might benefit from some comparison or contrast? Read on to consider some of the ways that these strategies can help you in revision.

Cause and Effect (or Effect and Cause)

Do you see a potential cause-and-effect relationship developing in your draft? The cause-and-effect pattern may be used to identify one or more causes followed by one or more effects or results. Or you may reverse this sequence and describe effects first and then the cause or causes. For example, the causes of water pollution might be followed by its effects on both humans and animals. You may use obvious transitions to clarify cause and effect, such as “What are the results? Here are some of them…” or you might simply use the words cause, effect, and result, to cue the reader about your about the relationships that you’re establishing.

Problem-Solution

At some point does your essay explore a problem or suggest a solution? The problem-solution pattern is commonly used in identifying something that’s wrong and in contemplating what might be done to remedy the situation. There are probably more ways to organize a problem-solution approach, but but here are three possibilities:

When the solution is stated at the end of the paper, the pattern is sometimes called the delayed proposal. For a hostile audience, it may be effective to describe the problem, show why other solutions do not work, and finally suggest the favored solution. You can emphasize the words problem and solution to signal these sections of your paper for your reader.

Chronology or Narrative

Do you need to develop support for a topic where telling a story can illustrate some important concept for your readers? Material arranged chronologically is explained as it occurs in time. A chronological or narrative method of development might help you find a way to add both interest and content to your essay. Material arranged chronologically is explained as it occurs in time. This pattern may be used to establish what has happened. Chronology or narrative can be a great way to introduce your essay by providing a background or history behind your topic. Or you may want to tell a story to develop one or more points in the body of your essay. You can use transitional words like then, next, and finally to make the parts of the chronology clear.

Comparison and Contrast

Are you trying to define something? Do you need your readers to understand what something is and what it is not? The comparison-and-contrast method of development is particularly useful in extending a definition, or anywhere you need to show how a subject is like or unlike another subject. For example, the statement is often made that drug abuse is a medical problem instead of a criminal justice issue. An author might attempt to prove this point by comparing drug addiction to AIDS, cancer, or heart disease to redefine the term “addiction” as a medical problem. A statement in opposition to this idea could just as easily establish contrast by explaining all the ways that addiction is different from what we traditionally understand as an illness. In seeking to establish comparison or contrast in your writing, some words or terms that might be useful are by contrast, in comparison, while, some, and others.

Summary

These four methods of development—cause and effect, problem-solution, chronology or narrative, and comparison and contrast—are just a few ways to organize and develop ideas and content in your essays. It’s important to note that they should not be a starting point for writers who want to write something authentic—something that they care deeply about. Instead, they can be a great way to help you look for what’s already happening with your topic or in a draft, to help you to write more, or to help you reorganize some parts of an essay that seem to lack connection or feel disjointed. Look for organizational patterns when you’re reading work by professional writers. Notice where they combine strategies (e.g., a problem-solution pattern that uses cause-and-effect organization, or a comparison-contrast pattern that uses narrative or chronology to develop similarities or differences). Pay attention to how different writers emphasize and develop their main ideas, and use what you find to inspire you in your own writing. Better yet, work on developing completely new patterns of your own.

Reference

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Patterns of Organization and Methods of Development

Patterns of organization can help your readers follow the ideas within your essay and your paragraphs, but they can also work as methods of development to help you recognize and further develop ideas and relationships in your writing. Here are some strategies that can help you with both organization and development in your essays.

Major Patterns of Organization

A fruit pie.

Read the following sentences:

How did it feel to read the above list? A bit confusing, I would guess. That’s because the steps for making a pie were not well organized, and the steps don’t include enough detail for us to know exactly what we should do. (Like what are the dry and liquid ingredients?) We all know that starting instructions from the beginning and giving each detailed step in the order it should happen is vital to having a good outcome, in this case a yummy pie! But it’s not always so simple to know how to organize or develop ideas, and sometimes there’s more than one way, which complicates things even further.

First, let’s take a look at a couple of ways to think about organization.

General to Specific or Specific to General

It might be useful to think about organizing your topic like a triangle:

Two triangles. The first is an inverted pyramid for General to Specific, the second is a pyramid for Specific to General.

The first triangle represents starting with the most general, big picture information first, moving then to more detailed and often more personal information later in the paper. The second triangle represents an organizational structure that starts with the specific, small scale information first and then moves to the more global, big picture stuff.

For example, if your topic is traffic in Vancouver, British Columbia, an essay that uses the general-to-specific organizational structure might begin this way:

Many people consider Vancouver, British Columbia, to be a relaxed place to live. They would be shocked to know how bad the traffic is traveling major arteries into the city and even driving around the city itself.

An essay that uses the specific-to-general structure might start like this:

Transit is crowded, parking is expensive, and vehicles stop and go through the main streets of the city of Vancouver, British Columbia, and that is just once travelers brave the crowded arteries to enter the city; Vancouver’s traffic problem does not lend itself to the relaxed atmosphere many believe the city to have.

What’s the difference between these two introductions? And how might they appeal to the intended audience for this essay in different ways? The first introduction is looking at the big picture of the problem and mentions pollution’s impact on all citizens in Portland, while the second introduction focuses on one specific family. The first helps readers see how vast the problem really is, and the second helps connect readers to a real family, making an emotional appeal from the very beginning. Neither introduction is necessarily better. You’ll choose one over the other based on the kind of tone you’d like to create and how you’d like to affect your audience. It’s completely up to you to make this decision.

Does the Triangle Mean the Essay Keeps Getting More Specific or More Broad until the Very End?

The triangle is kind of a general guide, meaning you’re allowed to move around within it all you want. For example, it’s possible that each of your paragraphs will be its own triangle, starting with the general or specific and moving out or in. However, if you begin very broadly, it might be effective to end your essay in a more specific, personal way. And if you begin with a personal story, consider ending your essay by touching on the global impact and importance of your topic.

Are There Other Ways to Think about Organizing My Ideas?

Yes! Rather than thinking about which of your ideas are most specific or personal or which are more broad or universal, you might consider one of the following ways of organizing your ideas:

The section on Methods of Development, below, offers more detail about some of these organizational patterns, along with some others.

Choose one of the following topics, and practice writing a few opening sentences like we did above, once using the general-to-specific format and once using the specific-to-general. Which do you like better? What audience would be attracted to which one? Share with peers to see how others tackled this challenge. How would you rewrite their sentences? Why? Discuss your changes and listen to how your peers have revised your sentences. Taking in other people’s ideas will help you see new ways to approach your own writing and thinking.
Topics:

Methods of Development

The methods of development covered here are best used as ways to look at what’s already happening in your draft and to consider how you might emphasize or expand on any existing patterns. You might already be familiar with some of these patterns because teachers will sometimes assign them as the purpose for writing an essay. For example, you might have been asked to write a cause-and-effect essay or a comparison-and-contrast essay.

It’s important to emphasize here that patterns of organization or methods of developing content usually happen naturally as a consequence of the way the writer engages with and organizes information while writing. That is to say, most writers don’t sit down and say, “I think I’ll write a cause-and-effect essay today.” Instead, a writer might be more likely to be interested in a topic, say, the state of drinking water in the local community, and as the writer begins to explore the topic, certain cause-and-effect relationships between environmental pollutants and the community water supply may begin to emerge.

So if these patterns just occur naturally in writing, what’s the use in knowing about them? Well, sometimes you might be revising a draft and notice that some of your paragraphs are a bit underdeveloped. Maybe they lack a clear topic, or maybe they lack support. In either case, you can look to these common methods of development to find ways to sharpen those vague topics or to add support where needed. Do you have a clear cause statement somewhere but you haven’t explored the effects? Are you lacking detail somewhere where a narrative story or historical chronology can help build reader interest and add support? Are you struggling to define an idea that might benefit from some comparison or contrast? Read on to consider some of the ways that these strategies can help you in revision.

Cause and Effect (or Effect and Cause)

Do you see a potential cause-and-effect relationship developing in your draft? The cause-and-effect pattern may be used to identify one or more causes followed by one or more effects or results. Or you may reverse this sequence and describe effects first and then the cause or causes. For example, the causes of water pollution might be followed by its effects on both humans and animals. You may use obvious transitions to clarify cause and effect, such as “What are the results? Here are some of them…” or you might simply use the words cause, effect, and result, to cue the reader about your about the relationships that you’re establishing.

Problem-Solution

At some point does your essay explore a problem or suggest a solution? The problem-solution pattern is commonly used in identifying something that’s wrong and in contemplating what might be done to remedy the situation. There are probably more ways to organize a problem-solution approach, but but here are three possibilities:

When the solution is stated at the end of the paper, the pattern is sometimes called the delayed proposal. For a hostile audience, it may be effective to describe the problem, show why other solutions do not work, and finally suggest the favored solution. You can emphasize the words problem and solution to signal these sections of your paper for your reader.

Chronology or Narrative

Do you need to develop support for a topic where telling a story can illustrate some important concept for your readers? Material arranged chronologically is explained as it occurs in time. A chronological or narrative method of development might help you find a way to add both interest and content to your essay. Material arranged chronologically is explained as it occurs in time. This pattern may be used to establish what has happened. Chronology or narrative can be a great way to introduce your essay by providing a background or history behind your topic. Or you may want to tell a story to develop one or more points in the body of your essay. You can use transitional words like then, next, and finally to make the parts of the chronology clear.

Comparison and Contrast

Are you trying to define something? Do you need your readers to understand what something is and what it is not? The comparison-and-contrast method of development is particularly useful in extending a definition, or anywhere you need to show how a subject is like or unlike another subject. For example, the statement is often made that drug abuse is a medical problem instead of a criminal justice issue. An author might attempt to prove this point by comparing drug addiction to AIDS, cancer, or heart disease to redefine the term “addiction” as a medical problem. A statement in opposition to this idea could just as easily establish contrast by explaining all the ways that addiction is different from what we traditionally understand as an illness. In seeking to establish comparison or contrast in your writing, some words or terms that might be useful are by contrast, in comparison, while, some, and others.

Summary

These four methods of development—cause and effect, problem-solution, chronology or narrative, and comparison and contrast—are just a few ways to organize and develop ideas and content in your essays. It’s important to note that they should not be a starting point for writers who want to write something authentic—something that they care deeply about. Instead, they can be a great way to help you look for what’s already happening with your topic or in a draft, to help you to write more, or to help you reorganize some parts of an essay that seem to lack connection or feel disjointed. Look for organizational patterns when you’re reading work by professional writers. Notice where they combine strategies (e.g., a problem-solution pattern that uses cause-and-effect organization, or a comparison-contrast pattern that uses narrative or chronology to develop similarities or differences). Pay attention to how different writers emphasize and develop their main ideas, and use what you find to inspire you in your own writing. Better yet, work on developing completely new patterns of your own.

Reference

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Formulas for IPhO 日本語版: Section 1

1: 数学

1.1: Taylor 展開

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1.8: 円周角

  1. 円周角は中心角の半分. よって，直角三角形の斜辺は その外接円の直径. もし四角形の対角の和が 180 度な らば，それは円に内接する.

1.9: 三角形の面樍

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Formulas for IPhO 日本語版: Section 1

1: 数学

1.1: Taylor 展開

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1.8: 円周角

  1. 円周角は中心角の半分. よって，直角三角形の斜辺は その外接円の直径. もし四角形の対角の和が 180 度な らば，それは円に内接する.

1.9: 三角形の面樍

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Formulas for IPhO 日本語版: Section 11

11: 量子力学

11.1:p=hk

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11.2: 干渉

  1. 干渉 : 波動光学のように.

11.3: 不確定性

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Formulas for IPhO 日本語版: Section 11

11: 量子力学

11.1:p=hk

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11.2: 干渉

  1. 干渉 : 波動光学のように.

11.3: 不確定性

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Formulas for IPhO 日本語版: Section 12

12: Kepler の法則

12.1: F & U

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12.2: Kepler の第一法則

  1. Kepler の第一法則 (2 質点の重力相互作用)：それぞ れの軌道は，系の質量中心に焦点を持つ楕円，双曲線, 放物線になる. これは Runge-Lenz ベクトルから得ら れる (ポイント 9).

12.3: Kepler の第二法則

  1. Kepler の第二法則（角運動量の保存）: 中心力が働く 場にある質点について，その位置ベクトルは単位時間 に一定の面積を描く.

12.4: Kepler の第三法則

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Formulas for IPhO 日本語版: Section 12

12: Kepler の法則

12.1: F & U

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12.2: Kepler の第一法則

  1. Kepler の第一法則 (2 質点の重力相互作用)：それぞ れの軌道は，系の質量中心に焦点を持つ楕円，双曲線, 放物線になる. これは Runge-Lenz ベクトルから得ら れる (ポイント 9).

12.3: Kepler の第二法則

  1. Kepler の第二法則（角運動量の保存）: 中心力が働く 場にある質点について，その位置ベクトルは単位時間 に一定の面積を描く.

12.4: Kepler の第三法則

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Formulas for IPhO 日本語版: Section 13

13: 相対性理論

13.1:Lorentz 変換

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Formulas for IPhO 日本語版: Section 13

13: 相対性理論

13.1:Lorentz 変換

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Formulas for IPhO 日本語版: Section 3

3: 運動学

3.1: 質点

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3.3: 曲線運動

  1. 曲線運動は，ポイント 1 と同じだが，ベクトルは線速 度，加速度，経路長に置き換える.

3.4: 剛体の運動

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3.7: 最短経路

  1. 最短経路を求めるには，Fermat と Huygens の原理が 使える.

3.8: ベクトル

  1. ベクトル（速度，加速度）を求めるには，その向きと （場合によっては傾いた）ある軸への射影を求めれば 充分.
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Formulas for IPhO 日本語版: Section 3

3: 運動学

3.1: 質点

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\\omega & =\\mathrm{d} \\varphi / \\mathrm{d} t, \\varepsilon=\\mathrm{d} \\omega / \\mathrm{d} t \\\\ \\boldsymbol{a} & =\\boldsymbol{\\tau} \\mathrm{d} v / \\mathrm{d} t+\\boldsymbol{n} v^2 / R \\end{aligned} ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"3.0241em","vertical-align":"-1.2621em"}}),s("span",{class:"mord"},[s("span",{class:"mtable"},[s("span",{class:"col-align-r"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.7621em"}},[s("span",{style:{top:"-3.9221em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"ω")])]),s("span",{style:{top:"-2.3979em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord 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3.3: 曲線運動

  1. 曲線運動は，ポイント 1 と同じだが，ベクトルは線速 度，加速度，経路長に置き換える.

3.4: 剛体の運動

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3.7: 最短経路

  1. 最短経路を求めるには，Fermat と Huygens の原理が 使える.

3.8: ベクトル

  1. ベクトル（速度，加速度）を求めるには，その向きと （場合によっては傾いた）ある軸への射影を求めれば 充分.
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Formulas for IPhO 日本語版: Section 4

4: 力学

4.1: 剛体の二次元的な平衡

  1. 剛体の二次元的な平衡 : 力についての 2 つの式とトル クについての 1 つの式. 1 （又は 2 ）個の力についての 式は 1（又は 2）個のトルクについての式で代用でき る. トルクの方が良い場合が多く，原点を適切に選択 することで「退屈な」力を消すことができる. もし 2 点 のみに力がかかっているならば，（正味の）力がかかっ ている直線は一致する. 3 点であれば, 3 つの直線は 1 点で交わる.

4.2: 垂直抗力

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Formulas for IPhO 日本語版: Section 4

4: 力学

4.1: 剛体の二次元的な平衡

  1. 剛体の二次元的な平衡 : 力についての 2 つの式とトル クについての 1 つの式. 1 （又は 2 ）個の力についての 式は 1（又は 2）個のトルクについての式で代用でき る. トルクの方が良い場合が多く，原点を適切に選択 することで「退屈な」力を消すことができる. もし 2 点 のみに力がかかっているならば，（正味の）力がかかっ ている直線は一致する. 3 点であれば, 3 つの直線は 1 点で交わる.

4.2: 垂直抗力

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Formulas for IPhO 日本語版: Section 5

5. 振動と波

5.1: 減衰振動

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Formulas for IPhO 日本語版: Section 5

5. 振動と波

5.1: 減衰振動

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Formulas for IPhO 日本語版: Section 6

6: 幾何光学，測光

6.1: Fermat 原理

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6.7: 像の位置を求める視差法

  1. 像の位置を求める視差法 : 目の位置と垂直に動かした ときに，鉛筆の先が像に対してずれないような位置を 探す.

6.8: レンズを通る光線の経路の幾何学的な描き方

  1. レンズを通る光線の経路の幾何学的な描き方：a) レン ズの中心を通る光線は屈折しない。b) 光軸に平行な光 線は焦点を通る，c) 屈折後, 初めに平行だった光線どうしは焦点面（焦点を通り光軸に垂直な平面）上で集 まる．d) 平面の像は平面であり，この 2 つの平面はレ ンズの平面上で交わる．

6.9: 光束

',5),M=s("ol",{start:"9"},[s("li",null,[a("光束 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"Φ")]),s("annotation",{encoding:"application/x-tex"},"\\Phi")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord"},"Φ")])])]),a(" [単位: lumen 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"),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"I"),s("mo",null,"="),s("mi",{mathvariant:"normal"},"Φ"),s("mi",{mathvariant:"normal"},"/"),s("mi",{mathvariant:"normal"},"Ω")]),s("annotation",{encoding:"application/x-tex"},"I=\\Phi / \\Omega")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"Φ/Ω")])])]),a(". 照度 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Formulas for IPhO 日本語版: Section 6

6: 幾何光学，測光

6.1: Fermat 原理

',3),r=s("ol",null,[s("li",null,[a("Fermat の原理 : 点 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"A")]),s("annotation",{encoding:"application/x-tex"},"A")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal"},"A")])])]),a(" から "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B")]),s("annotation",{encoding:"application/x-tex"},"B")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B")])])]),a(" への波の経路は波の移動 時間が最も短いもの.")])],-1),p=s("h3",{id:"_6-2-snell-法則",tabindex:"-1"},[a("6.2: Snell 法則 "),s("a",{class:"header-anchor",href:"#_6-2-snell-法則","aria-hidden":"true"},"#")],-1),c=s("ol",{start:"2"},[s("li",null,"Snell の法則 :")],-1),h=s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mi",null,"sin"),s("mo",null,"⁡"),s("msub",null,[s("mi",null,"α"),s("mn",null,"1")]),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"sin"),s("mo",null,"⁡"),s("msub",null,[s("mi",null,"α"),s("mn",null,"2")]),s("mo",null,"="),s("msub",null,[s("mi",null,"n"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"/"),s("msub",null,[s("mi",null,"n"),s("mn",null,"1")]),s("mo",null,"="),s("msub",null,[s("mi",null,"v"),s("mn",null,"1")]),s("mi",{mathvariant:"normal"},"/"),s("msub",null,[s("mi",null,"v"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},".")]),s("annotation",{encoding:"application/x-tex"},"\\sin \\alpha_1 / \\sin \\alpha_2=n_2 / n_1=v_1 / v_2 . 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6.7: 像の位置を求める視差法

  1. 像の位置を求める視差法 : 目の位置と垂直に動かした ときに，鉛筆の先が像に対してずれないような位置を 探す.

6.8: レンズを通る光線の経路の幾何学的な描き方

  1. レンズを通る光線の経路の幾何学的な描き方：a) レン ズの中心を通る光線は屈折しない。b) 光軸に平行な光 線は焦点を通る，c) 屈折後, 初めに平行だった光線どうしは焦点面（焦点を通り光軸に垂直な平面）上で集 まる．d) 平面の像は平面であり，この 2 つの平面はレ ンズの平面上で交わる．

6.9: 光束

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Formulas for IPhO 日本語版: Section 7

7: 波動光学

7.1: Huygens の原理に基づいた回折

  1. Huygens の原理に基づいた回折 : 障害物が波面を切断 すると波面は小さな断片に分割され，それが仮想的な 点波源となり，観測点での波の振幅はこれらの波源か らの寄与の重ね合わせとなる.

7.2: 二重スリット

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Formulas for IPhO 日本語版: Section 7

7: 波動光学

7.1: Huygens の原理に基づいた回折

  1. Huygens の原理に基づいた回折 : 障害物が波面を切断 すると波面は小さな断片に分割され，それが仮想的な 点波源となり，観測点での波の振幅はこれらの波源か らの寄与の重ね合わせとなる.

7.2: 二重スリット

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Formulas for IPhO 日本語版: Section 8

8: 電気回路

8.1: V=I R, P=V I

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8.4: 無限につながる抵抗

  1. 無限につながる抵抗 : 無限に続く格子の隣り合う節点 間で，自己相似性を使う。鏡像法の一般化された方法.

8.5: 交流回路

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Formulas for IPhO 日本語版: Section 8

8: 電気回路

8.1: V=I R, P=V I

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8.4: 無限につながる抵抗

  1. 無限につながる抵抗 : 無限に続く格子の隣り合う節点 間で，自己相似性を使う。鏡像法の一般化された方法.

8.5: 交流回路

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Formulas for IPhO 日本語版: Section 9

9: 電磁気学

9.1: Coulomb の法則

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\\sum_{i9.10: 一様に帯電した球面や円筒面の各部分の間に働く力
  1. 一様に帯電した球面や円筒面の各部分の間に働く力 : 帯電による力を静水圧による力に置き換える.

9.11: 全ての電荷

',3),B=s("ol",{start:"12"},[s("li",null,[a("全ての電荷が距離 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])]),a(" にある場合（例えば，不均一に帯 電した球やリングの中心） "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"ϕ"),s("mi",null,"ϕ"),s("mo",null,"="),s("mi",null,"k"),s("mi",null,"Q"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"\\phi \\phi=k Q / r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"ϕϕ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord mathnormal"},"Q"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])])])],-1),L=l('

9.12: 外部電荷

  1. 外部電荷によって引き起こされる正味の電荷（又は電 位）を求めるには, 電荷を「出現」させて問題を対称的 にし，重ね合わせの原理を用いる.

9.14: 導体

',3),I=s("ol",{start:"14"},[s("li",null,[a("導体は電荷や電場を遮蔽する．例えば，中空の球体の 内部の電荷分布は外から見えない（あたかも "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"Q")]),s("annotation",{encoding:"application/x-tex"},"Q")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8778em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"Q")])])]),a(" という 電荷を持った導電性の球があるように見える).")])],-1),S=s("h3",{id:"_9-15-静電容量",tabindex:"-1"},[a("9.15: 静電容量 "),s("a",{class:"header-anchor",href:"#_9-15-静電容量","aria-hidden":"true"},"#")],-1),E=s("ol",{start:"15"},[s("li",null,[a("静電容量: 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9.20: 鏡像法

  1. 鏡像法 : 接地された（磁石の場合は超電導の）平面が鏡 の役割をする. 接地された（又は孤立した）球体の場 は, 球体の内部にある 1 つ（又は 2 つ）の架空の電荷 のつくる場として求められる. 平面導波管（金属板の 間のスリット）内の場は, 電磁平面波の重ね合わせと して求められる.

9.21: 一様（電）場中の球 (円柱) の分極

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Formulas for IPhO 日本語版: Section 9

9: 電磁気学

9.1: Coulomb の法則

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\\sum_{i9.10: 一様に帯電した球面や円筒面の各部分の間に働く力
  1. 一様に帯電した球面や円筒面の各部分の間に働く力 : 帯電による力を静水圧による力に置き換える.

9.11: 全ての電荷

',3),B=s("ol",{start:"12"},[s("li",null,[a("全ての電荷が距離 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])]),a(" にある場合（例えば，不均一に帯 電した球やリングの中心） "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"ϕ"),s("mi",null,"ϕ"),s("mo",null,"="),s("mi",null,"k"),s("mi",null,"Q"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"\\phi \\phi=k Q / r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"ϕϕ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord mathnormal"},"Q"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])])])],-1),L=l('

9.12: 外部電荷

  1. 外部電荷によって引き起こされる正味の電荷（又は電 位）を求めるには, 電荷を「出現」させて問題を対称的 にし，重ね合わせの原理を用いる.

9.14: 導体

',3),I=s("ol",{start:"14"},[s("li",null,[a("導体は電荷や電場を遮蔽する．例えば，中空の球体の 内部の電荷分布は外から見えない（あたかも "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"Q")]),s("annotation",{encoding:"application/x-tex"},"Q")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8778em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"Q")])])]),a(" という 電荷を持った導電性の球があるように見える).")])],-1),S=s("h3",{id:"_9-15-静電容量",tabindex:"-1"},[a("9.15: 静電容量 "),s("a",{class:"header-anchor",href:"#_9-15-静電容量","aria-hidden":"true"},"#")],-1),E=s("ol",{start:"15"},[s("li",null,[a("静電容量: 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9.20: 鏡像法

  1. 鏡像法 : 接地された（磁石の場合は超電導の）平面が鏡 の役割をする. 接地された（又は孤立した）球体の場 は, 球体の内部にある 1 つ（又は 2 つ）の架空の電荷 のつくる場として求められる. 平面導波管（金属板の 間のスリット）内の場は, 電磁平面波の重ね合わせと して求められる.

9.21: 一様（電）場中の球 (円柱) の分極

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\\sum_{i2023-2-27: Vocabulary

This table of vocabularies are from "Sadlier Vocabulary Workshop-Level G (Unit 4)" with their corresponding textbook definitions and part of speeches (from some of them) made into a collection.

VocabularyDefinition
Atrophy(n.) the wasting away of a body organ or tissue; any progressive decline or failure; (v.) to waste away
BastionA fortified place, stronghold
ConcordA state of agreement, harmony, unanimity; a treaty, pact, covenant
Consummate(adj.) complete or perfect in the highest degree; (v.) to bring to a state of completion or perfection
Disarray(n.) disorder, confusion; (v.) to throw into disorder
ExigencyUrgency, pressure; urgent demand, pressing need; an emergency
FlotsamFloating debris; homeless, impoverished people
FreneticFrenzied, highly agitated
GleanTo gather bit by bit; to gather small quantities of grain left in a field by the reapers.
Grouse(n.) A type of game bird; a complaint; (v.) to complain, grumble
IncarcerateTo imprison, confine, jail
Incumbent(adj.) obligatory, required; (n.) one who holds a specific office at the time spoken of
JocularHumorous, jesting, jolly, joking
LudicrousRidiculous, laughable, absurd
MordantBiting or caustic in thought, manner, or style; sharply or bitterly harsh.
Nettle(n.) a prickly or stinging plant; (v.) to arouse displeasure, impatience, or anger; to vex or irritate severely
PecuniaryConsisting of or measured in money; of or related to money
PusillanimousContemptibly cowardly or mean-spirited
RecumbentIn a reclining position, lying down, in the posture of one sleeping or resting.
StratagemA scheme to outwit or deceive an opponent or to gain and end.

Reference

',4),i=[d];function n(s,l,c,u,p,h){return r(),e("div",null,i)}const b=t(a,[["render",n]]);export{y as __pageData,b as default}; +import{_ as t,c as e,o as r,d as o}from"./app.b4df1b52.js";const y=JSON.parse('{"title":"2023-2-27: Vocabulary","description":"Vocabulary list collected for 2023-2-27","frontmatter":{"title":"2023-2-27: Vocabulary","description":"Vocabulary list collected for 2023-2-27"},"headers":[],"relativePath":"academic/vocabulary/2023/02/2023-02-27.md","lastUpdated":1679745767000}'),a={name:"academic/vocabulary/2023/02/2023-02-27.md"},d=o('

2023-2-27: Vocabulary

This table of vocabularies are from "Sadlier Vocabulary Workshop-Level G (Unit 4)" with their corresponding textbook definitions and part of speeches (from some of them) made into a collection.

VocabularyDefinition
Atrophy(n.) the wasting away of a body organ or tissue; any progressive decline or failure; (v.) to waste away
BastionA fortified place, stronghold
ConcordA state of agreement, harmony, unanimity; a treaty, pact, covenant
Consummate(adj.) complete or perfect in the highest degree; (v.) to bring to a state of completion or perfection
Disarray(n.) disorder, confusion; (v.) to throw into disorder
ExigencyUrgency, pressure; urgent demand, pressing need; an emergency
FlotsamFloating debris; homeless, impoverished people
FreneticFrenzied, highly agitated
GleanTo gather bit by bit; to gather small quantities of grain left in a field by the reapers.
Grouse(n.) A type of game bird; a complaint; (v.) to complain, grumble
IncarcerateTo imprison, confine, jail
Incumbent(adj.) obligatory, required; (n.) one who holds a specific office at the time spoken of
JocularHumorous, jesting, jolly, joking
LudicrousRidiculous, laughable, absurd
MordantBiting or caustic in thought, manner, or style; sharply or bitterly harsh.
Nettle(n.) a prickly or stinging plant; (v.) to arouse displeasure, impatience, or anger; to vex or irritate severely
PecuniaryConsisting of or measured in money; of or related to money
PusillanimousContemptibly cowardly or mean-spirited
RecumbentIn a reclining position, lying down, in the posture of one sleeping or resting.
StratagemA scheme to outwit or deceive an opponent or to gain and end.

Reference

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1: Installation

Before you start using this plugin, make sure you have already installed the default markdown-it parser; if not, please run the following command or refer to the official markdown-it documentation.

sh
$ npm install markdown-it --save
+import{_ as l,c as e,o as t,a as s,b as a,d as n}from"./app.b4df1b52.js";const k=JSON.parse(`{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China","frontmatter":{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China"},"headers":[{"level":2,"title":"1: Installation","slug":"_1-installation","link":"#_1-installation","children":[]},{"level":2,"title":"2: Usage","slug":"_2-usage","link":"#_2-usage","children":[{"level":3,"title":"3: Configuration","slug":"_3-configuration","link":"#_3-configuration","children":[]}]},{"level":2,"title":"4: Examples","slug":"_4-examples","link":"#_4-examples","children":[{"level":3,"title":"4.1: Inline math","slug":"_4-1-inline-math","link":"#_4-1-inline-math","children":[]},{"level":3,"title":"4.2: Blocked math","slug":"_4-2-blocked-math","link":"#_4-2-blocked-math","children":[]}]},{"level":2,"title":"5: Syntax","slug":"_5-syntax","link":"#_5-syntax","children":[]},{"level":2,"title":"6: Supported math syntax","slug":"_6-supported-math-syntax","link":"#_6-supported-math-syntax","children":[]}],"relativePath":"application/markdown-it-katex/how-to-use.md","lastUpdated":1679745767000}`),p={name:"application/markdown-it-katex/how-to-use.md"},o=s("h1",{id:"andatoshiki-markdown-it-katex",tabindex:"-1"},[a("@andatoshiki/markdown-it-katex "),s("a",{class:"header-anchor",href:"#andatoshiki-markdown-it-katex","aria-hidden":"true"},"#")],-1),r=s("blockquote",null,[s("p",null,[a("Add graceful "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mtext",null,"KaTeX")]),s("annotation",{encoding:"application/x-tex"},"\\KaTeX")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8988em","vertical-align":"-0.2155em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"K"),s("span",{class:"mspace",style:{"margin-right":"-0.17em"}}),s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.6833em"}},[s("span",{style:{top:"-2.905em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm mtight sizing reset-size6 size3"},"A")])])])])]),s("span",{class:"mspace",style:{"margin-right":"-0.15em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"T"),s("span",{class:"mspace",style:{"margin-right":"-0.1667em"}}),s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.4678em"}},[s("span",{style:{top:"-2.7845em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm"},"E")])])]),s("span",{class:"vlist-s"},"​")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2155em"}},[s("span")])])]),s("span",{class:"mspace",style:{"margin-right":"-0.125em"}}),s("span",{class:"mord textrm"},"X")])])])])]),a(" rendering to your Markdown like a charm with "),s("code",null,"markdown-it"),a(" plugin.")])],-1),c=n(`
1: Installation 
Before you start using this plugin, make sure you have already installed the default markdown-it parser; if not, please run the following command or refer to the official markdown-it documentation.
sh
$ npm install markdown-it --save
 
$ npm install markdown-it --save
-
First install package with your preferred package manager (npm, yarn, pnpm), or include javascript before the closing </body> for markdown-it-katex's core utils to be loaded for the static page.
sh
$ npm install -D @andatoshiki/markdown-it-katex
+
First install package with your preferred package manager (npm, yarn, pnpm), or include javascript before the closing </body> for markdown-it-katex's core utils to be loaded for the static page.
sh
$ npm install -D @andatoshiki/markdown-it-katex
 
$ npm install -D @andatoshiki/markdown-it-katex
 
sh
$ yarn add --dev @andatoshiki/markdown-it-katex
 
$ yarn add --dev @andatoshiki/markdown-it-katex
@@ -12,7 +12,7 @@ import{_ as l,c as e,o as t,a as s,b as a,d as n}from"./app.b4df1b52.js";const k
 
<!-- your other body contents ... -->
     <script src="https://unpkg.com/@andatoshiki/markdown-it-katex@0.0.3/markdown-it-katex.min.js"></script>
 </body>
-
Including KaTeX CSS is necessary in the way you are convenient with, either link the stylesheet from a third party CDN into the local HTML <head> tag or import it into a currently linked CSS stylesheets to enable styles for KaTeX globally as follows,
Or, you could clone or download the entire repository source of KaTeX and self load the fonts/styles/scripts locally, but if you prefer loading from third-party CDN with faster load speed when deployed to save your server resources, the following CDN links might be your choice, you can always switch to other platforms based on your need.
html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
+
Including KaTeX CSS is necessary in the way you are convenient with, either link the stylesheet from a third party CDN into the local HTML <head> tag or import it into a currently linked CSS stylesheets to enable styles for KaTeX globally as follows,
Or, you could clone or download the entire repository source of KaTeX and self load the fonts/styles/scripts locally, but if you prefer loading from third-party CDN with faster load speed when deployed to save your server resources, the following CDN links might be your choice, you can always switch to other platforms based on your need.
html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
 
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
 
html
<link rel="stylesheet" href="https://gcore.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
 
<link rel="stylesheet" href="https://gcore.jsdelivr.net/npm/katex@0.16/dist/katex.min.css" />
@@ -28,7 +28,7 @@ import{_ as l,c as e,o as t,a as s,b as a,d as n}from"./app.b4df1b52.js";const k
 @import 'https://cdnjs.toshiki.dev/ajax/libs/KaTeX/0.16.0/katex.min.css';
 
If you are using the default markdown-it parser, I personally recommend that you use the GitHub markdown CSS (github-markdown-css) for styling your HTML output with a similar style replica of GitHub's markdown styling to your familiarity.
html
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/github-markdown-css@5.2.0/github-markdown.min.css" />
 
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/github-markdown-css@5.2.0/github-markdown.min.css" />
-
This forked project maintained by Anda Toshiki comes with the update of KaTeX components with higher style version support (this documentation uses KaTeX version 16.0, without hassels), later versions may works, but no guarantees are given by the developers, if you are not obsessed with the latest released version, 16.0 may fits your need for loading KaTeX on a personal blog site or small educational sites; yet it should work fully functionally.
Warning
Since this project is a fork of the original markdown-it-katex project that hasn't been receiving any active updates of its code source for years, the latest katex style version supported is somewhere around ver. 0.9.0 which clearly is outdated and results in broken styles with overflowing and other potential bug presents.
2: Usage 
RTo render equations, you need to include the markdown-it-katex plugin in the markdown-it components in your JavaScript or TypeScript file as follows,
js
var md = require('markdown-it')(),
+
This forked project maintained by Anda Toshiki comes with the update of KaTeX components with higher style version support (this documentation uses KaTeX version 16.0, without hassels), later versions may works, but no guarantees are given by the developers, if you are not obsessed with the latest released version, 16.0 may fits your need for loading KaTeX on a personal blog site or small educational sites; yet it should work fully functionally.
Warning
Since this project is a fork of the original markdown-it-katex project that hasn't been receiving any active updates of its code source for years, the latest katex style version supported is somewhere around ver. 0.9.0 which clearly is outdated and results in broken styles with overflowing and other potential bug presents.
2: Usage 
RTo render equations, you need to include the markdown-it-katex plugin in the markdown-it components in your JavaScript or TypeScript file as follows,
js
var md = require('markdown-it')(),
     mk = require('andatoshiki/markdown-it-katex')
 
 md.use(mk)
diff --git a/assets/application_markdown-it-katex_how-to-use.md.86b38519.lean.js b/assets/application_markdown-it-katex_how-to-use.md.93aa4553.lean.js
similarity index 99%
rename from assets/application_markdown-it-katex_how-to-use.md.86b38519.lean.js
rename to assets/application_markdown-it-katex_how-to-use.md.93aa4553.lean.js
index 7bf1cebd..0e6c3b1b 100644
--- a/assets/application_markdown-it-katex_how-to-use.md.86b38519.lean.js
+++ b/assets/application_markdown-it-katex_how-to-use.md.93aa4553.lean.js
@@ -1,4 +1,4 @@
-import{_ as l,c as e,o as t,a as s,b as a,d as n}from"./app.b4df1b52.js";const k=JSON.parse(`{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China","frontmatter":{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China"},"headers":[{"level":2,"title":"1: Installation","slug":"_1-installation","link":"#_1-installation","children":[]},{"level":2,"title":"2: Usage","slug":"_2-usage","link":"#_2-usage","children":[{"level":3,"title":"3: Configuration","slug":"_3-configuration","link":"#_3-configuration","children":[]}]},{"level":2,"title":"4: Examples","slug":"_4-examples","link":"#_4-examples","children":[{"level":3,"title":"4.1: Inline math","slug":"_4-1-inline-math","link":"#_4-1-inline-math","children":[]},{"level":3,"title":"4.2: Blocked math","slug":"_4-2-blocked-math","link":"#_4-2-blocked-math","children":[]}]},{"level":2,"title":"5: Syntax","slug":"_5-syntax","link":"#_5-syntax","children":[]},{"level":2,"title":"6: Supported math syntax","slug":"_6-supported-math-syntax","link":"#_6-supported-math-syntax","children":[]}],"relativePath":"application/markdown-it-katex/how-to-use.md","lastUpdated":1679649941000}`),p={name:"application/markdown-it-katex/how-to-use.md"},o=s("h1",{id:"andatoshiki-markdown-it-katex",tabindex:"-1"},[a("@andatoshiki/markdown-it-katex "),s("a",{class:"header-anchor",href:"#andatoshiki-markdown-it-katex","aria-hidden":"true"},"#")],-1),r=s("blockquote",null,[s("p",null,[a("Add graceful "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mtext",null,"KaTeX")]),s("annotation",{encoding:"application/x-tex"},"\\KaTeX")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8988em","vertical-align":"-0.2155em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"K"),s("span",{class:"mspace",style:{"margin-right":"-0.17em"}}),s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.6833em"}},[s("span",{style:{top:"-2.905em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm mtight sizing reset-size6 size3"},"A")])])])])]),s("span",{class:"mspace",style:{"margin-right":"-0.15em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"T"),s("span",{class:"mspace",style:{"margin-right":"-0.1667em"}}),s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.4678em"}},[s("span",{style:{top:"-2.7845em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm"},"E")])])]),s("span",{class:"vlist-s"},"​")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2155em"}},[s("span")])])]),s("span",{class:"mspace",style:{"margin-right":"-0.125em"}}),s("span",{class:"mord textrm"},"X")])])])])]),a(" rendering to your Markdown like a charm with "),s("code",null,"markdown-it"),a(" plugin.")])],-1),c=n("",23),i=s("p",null,[a("rendered output equation as follows, "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("msqrt",null,[s("mrow",null,[s("mn",null,"3"),s("mi",null,"x"),s("mo",null,"−"),s("mn",null,"1")])]),s("mo",null,"+"),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,"+"),s("mi",null,"x"),s("msup",null,[s("mo",{stretchy:"false"},")"),s("mn",null,"2")])]),s("annotation",{encoding:"application/x-tex"},"\\sqrt{3x-1}+(1+x)^2")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.04em","vertical-align":"-0.1744em"}}),s("span",{class:"mord sqrt"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8656em"}},[s("span",{class:"svg-align",style:{top:"-3em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord",style:{"padding-left":"0.833em"}},[s("span",{class:"mord"},"3"),s("span",{class:"mord mathnormal"},"x"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"−"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord"},"1")])]),s("span",{style:{top:"-2.8256em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"hide-tail",style:{"min-width":"0.853em",height:"1.08em"}},[s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"400em",height:"1.08em",viewBox:"0 0 400000 1080",preserveAspectRatio:"xMinYMin slice"},[s("path",{d:`M95,702
+import{_ as l,c as e,o as t,a as s,b as a,d as n}from"./app.b4df1b52.js";const k=JSON.parse(`{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China","frontmatter":{"title":"@andatoshiki/markdown-it-katex","description":"Documentation for Toshiki's markdown-it-katex fork as an alternative for GitHub readme mirror in case site inaccessibility due to SNI interference by GFW for users in China"},"headers":[{"level":2,"title":"1: Installation","slug":"_1-installation","link":"#_1-installation","children":[]},{"level":2,"title":"2: Usage","slug":"_2-usage","link":"#_2-usage","children":[{"level":3,"title":"3: Configuration","slug":"_3-configuration","link":"#_3-configuration","children":[]}]},{"level":2,"title":"4: Examples","slug":"_4-examples","link":"#_4-examples","children":[{"level":3,"title":"4.1: Inline math","slug":"_4-1-inline-math","link":"#_4-1-inline-math","children":[]},{"level":3,"title":"4.2: Blocked math","slug":"_4-2-blocked-math","link":"#_4-2-blocked-math","children":[]}]},{"level":2,"title":"5: Syntax","slug":"_5-syntax","link":"#_5-syntax","children":[]},{"level":2,"title":"6: Supported math syntax","slug":"_6-supported-math-syntax","link":"#_6-supported-math-syntax","children":[]}],"relativePath":"application/markdown-it-katex/how-to-use.md","lastUpdated":1679745767000}`),p={name:"application/markdown-it-katex/how-to-use.md"},o=s("h1",{id:"andatoshiki-markdown-it-katex",tabindex:"-1"},[a("@andatoshiki/markdown-it-katex "),s("a",{class:"header-anchor",href:"#andatoshiki-markdown-it-katex","aria-hidden":"true"},"#")],-1),r=s("blockquote",null,[s("p",null,[a("Add graceful "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mtext",null,"KaTeX")]),s("annotation",{encoding:"application/x-tex"},"\\KaTeX")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8988em","vertical-align":"-0.2155em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"K"),s("span",{class:"mspace",style:{"margin-right":"-0.17em"}}),s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.6833em"}},[s("span",{style:{top:"-2.905em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm mtight sizing reset-size6 size3"},"A")])])])])]),s("span",{class:"mspace",style:{"margin-right":"-0.15em"}}),s("span",{class:"mord text"},[s("span",{class:"mord textrm"},"T"),s("span",{class:"mspace",style:{"margin-right":"-0.1667em"}}),s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.4678em"}},[s("span",{style:{top:"-2.7845em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord textrm"},"E")])])]),s("span",{class:"vlist-s"},"​")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2155em"}},[s("span")])])]),s("span",{class:"mspace",style:{"margin-right":"-0.125em"}}),s("span",{class:"mord textrm"},"X")])])])])]),a(" rendering to your Markdown like a charm with "),s("code",null,"markdown-it"),a(" plugin.")])],-1),c=n("",23),i=s("p",null,[a("rendered output equation as follows, "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("msqrt",null,[s("mrow",null,[s("mn",null,"3"),s("mi",null,"x"),s("mo",null,"−"),s("mn",null,"1")])]),s("mo",null,"+"),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,"+"),s("mi",null,"x"),s("msup",null,[s("mo",{stretchy:"false"},")"),s("mn",null,"2")])]),s("annotation",{encoding:"application/x-tex"},"\\sqrt{3x-1}+(1+x)^2")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.04em","vertical-align":"-0.1744em"}}),s("span",{class:"mord sqrt"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8656em"}},[s("span",{class:"svg-align",style:{top:"-3em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord",style:{"padding-left":"0.833em"}},[s("span",{class:"mord"},"3"),s("span",{class:"mord mathnormal"},"x"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"−"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord"},"1")])]),s("span",{style:{top:"-2.8256em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"hide-tail",style:{"min-width":"0.853em",height:"1.08em"}},[s("svg",{xmlns:"http://www.w3.org/2000/svg",width:"400em",height:"1.08em",viewBox:"0 0 400000 1080",preserveAspectRatio:"xMinYMin slice"},[s("path",{d:`M95,702
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diff --git a/assets/application_markdown-it-katex_support-function.md.80d3ff38.js b/assets/application_markdown-it-katex_support-function.md.8824ed46.js
similarity index 99%
rename from assets/application_markdown-it-katex_support-function.md.80d3ff38.js
rename to assets/application_markdown-it-katex_support-function.md.8824ed46.js
index 48b84cbb..3366903f 100644
--- a/assets/application_markdown-it-katex_support-function.md.80d3ff38.js
+++ b/assets/application_markdown-it-katex_support-function.md.8824ed46.js
@@ -1,4 +1,4 @@
-import{_ as e,c as l,a as s,b as a,d as t,o as n}from"./app.b4df1b52.js";const yt=JSON.parse('{"title":"KaTeX: Supported functions","description":"Supported functions within KaTeX syntaxes.","frontmatter":{"title":"KaTeX: Supported functions","description":"Supported functions within KaTeX syntaxes."},"headers":[{"level":2,"title":"1: Accents","slug":"_1-accents","link":"#_1-accents","children":[]},{"level":2,"title":"2: Delimiters","slug":"_2-delimiters","link":"#_2-delimiters","children":[]},{"level":2,"title":"3: Environments","slug":"_3-environments","link":"#_3-environments","children":[]},{"level":2,"title":"4: HTML","slug":"_4-html","link":"#_4-html","children":[]},{"level":2,"title":"5: Letters and Unicode","slug":"_5-letters-and-unicode","link":"#_5-letters-and-unicode","children":[]},{"level":2,"title":"6: Layout","slug":"_6-layout","link":"#_6-layout","children":[{"level":3,"title":"6.1: Annotation","slug":"_6-1-annotation","link":"#_6-1-annotation","children":[]},{"level":3,"title":"6.2: Line Breaks","slug":"_6-2-line-breaks","link":"#_6-2-line-breaks","children":[]},{"level":3,"title":"6.3: Vertical Layout","slug":"_6-3-vertical-layout","link":"#_6-3-vertical-layout","children":[]},{"level":3,"title":"6.4: Overlap and Spacing","slug":"_6-4-overlap-and-spacing","link":"#_6-4-overlap-and-spacing","children":[]}]},{"level":2,"title":"7: Logic and Set Theory","slug":"_7-logic-and-set-theory","link":"#_7-logic-and-set-theory","children":[]},{"level":2,"title":"8: Macros","slug":"_8-macros","link":"#_8-macros","children":[]},{"level":2,"title":"9: Operators","slug":"_9-operators","link":"#_9-operators","children":[{"level":3,"title":"9.1: Big Operators","slug":"_9-1-big-operators","link":"#_9-1-big-operators","children":[]},{"level":3,"title":"9.2: Binary Operators","slug":"_9-2-binary-operators","link":"#_9-2-binary-operators","children":[]},{"level":3,"title":"9.3: Fractions and Binomials","slug":"_9-3-fractions-and-binomials","link":"#_9-3-fractions-and-binomials","children":[]},{"level":3,"title":"9.4: Math Operators","slug":"_9-4-math-operators","link":"#_9-4-math-operators","children":[]},{"level":3,"title":"9.5: \\\\sqrt","slug":"_9-5-sqrt","link":"#_9-5-sqrt","children":[]}]},{"level":2,"title":"10: Relations","slug":"_10-relations","link":"#_10-relations","children":[{"level":3,"title":"10.1: Negated Relations","slug":"_10-1-negated-relations","link":"#_10-1-negated-relations","children":[]},{"level":3,"title":"10.2: Arrows","slug":"_10-2-arrows","link":"#_10-2-arrows","children":[]}]},{"level":2,"title":"11: Style, Color, Size, and Font","slug":"_11-style-color-size-and-font","link":"#_11-style-color-size-and-font","children":[]},{"level":2,"title":"12: Symbols and Punctuation","slug":"_12-symbols-and-punctuation","link":"#_12-symbols-and-punctuation","children":[]},{"level":2,"title":"13: Units","slug":"_13-units","link":"#_13-units","children":[]}],"relativePath":"application/markdown-it-katex/support-function.md","lastUpdated":1679649941000}'),m={name:"application/markdown-it-katex/support-function.md"},i=t('
KaTeX: Supported function 
note
This is an direct shameful copy of the documentation pulled from KaTeX documentation, I do not own any of the content below on behalf of this part of the documentation, the table might be outdated as versions migrates, please also refer to KaTeX's official documentation.
This following is a list of TeX functions supported by KaTeX. It is sorted into logical groups.
There is a similar Support Table on the next page, sorted alphabetically in am more intuitive way with the lists both supported and un-supported functions, viewing both tables are suggested comprehensibly and interchangeably is highly suggested.
1: Accents 
',5),c=s("thead",null,[s("tr",null,[s("th",{style:{"text-align":"left"}}),s("th",{style:{"text-align":"left"}}),s("th",{style:{"text-align":"left"}})])],-1),p=s("tr",null,[s("td",{style:{"text-align":"left"}},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("msup",null,[s("mi",null,"a"),s("mo",{mathvariant:"normal",lspace:"0em",rspace:"0em"},"′")])]),s("annotation",{encoding:"application/x-tex"},"a'")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7519em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"a"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.7519em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 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KaTeX: Supported function 
note
This is an direct shameful copy of the documentation pulled from KaTeX documentation, I do not own any of the content below on behalf of this part of the documentation, the table might be outdated as versions migrates, please also refer to KaTeX's official documentation.
This following is a list of TeX functions supported by KaTeX. It is sorted into logical groups.
There is a similar Support Table on the next page, sorted alphabetically in am more intuitive way with the lists both supported and un-supported functions, viewing both tables are suggested comprehensibly and interchangeably is highly suggested.
1: Accents 
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KaTeX: Support table 
note
This is an direct shameful copy of the documentation pulled from KaTeX documentation, I do not own any of the content below on behalf of this part of the documentation, the table might be outdated as versions migrates, please also refer to KaTeX's official documentation.
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KaTeX: Support table 
note
This is an direct shameful copy of the documentation pulled from KaTeX documentation, I do not own any of the content below on behalf of this part of the documentation, the table might be outdated as versions migrates, please also refer to KaTeX's official documentation.
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similarity index 99%
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diff --git a/assets/getting-started.md.e767a449.js b/assets/getting-started.md.8714bbcf.js
similarity index 99%
rename from assets/getting-started.md.e767a449.js
rename to assets/getting-started.md.8714bbcf.js
index ab7a7edb..a171b4df 100644
--- a/assets/getting-started.md.e767a449.js
+++ b/assets/getting-started.md.8714bbcf.js
@@ -1,4 +1,4 @@
-import{_ as s,c as a,o as n,d as o}from"./app.b4df1b52.js";const h=JSON.parse('{"title":"Git push results in \\"Authentication Failed”","description":"","frontmatter":{"title":"Git push results in \\"Authentication Failed”","author":"Anda Toshiki","date":"2023/2/21/ 10:54","editLink":true,"lastUpdated":true},"headers":[{"level":2,"title":"Issue","slug":"issue","link":"#issue","children":[]},{"level":2,"title":"Solution","slug":"solution","link":"#solution","children":[{"level":3,"title":"Solution 1","slug":"solution-1","link":"#solution-1","children":[]},{"level":3,"title":"Solution 2","slug":"solution-2","link":"#solution-2","children":[]}]}],"relativePath":"getting-started.md","lastUpdated":1679649941000}'),l={name:"getting-started.md"},e=o(`
Git push results in "Authentication Failed” 
Issue 
bash
$ git push
+import{_ as s,c as a,o as n,d as o}from"./app.b4df1b52.js";const h=JSON.parse('{"title":"Git push results in \\"Authentication Failed”","description":"","frontmatter":{"title":"Git push results in \\"Authentication Failed”","author":"Anda Toshiki","date":"2023/2/21/ 10:54","editLink":true,"lastUpdated":true},"headers":[{"level":2,"title":"Issue","slug":"issue","link":"#issue","children":[]},{"level":2,"title":"Solution","slug":"solution","link":"#solution","children":[{"level":3,"title":"Solution 1","slug":"solution-1","link":"#solution-1","children":[]},{"level":3,"title":"Solution 2","slug":"solution-2","link":"#solution-2","children":[]}]}],"relativePath":"getting-started.md","lastUpdated":1679745767000}'),l={name:"getting-started.md"},e=o(`
Git push results in "Authentication Failed” 
Issue 
bash
$ git push
 Username for 'https://github.com': \${{ GITHUB_USERNAME }}
 Password for 'https://andatoshiki@github.com': \${{ GITHUB_PASSWORD }} # or GitHub personal access token
 remote: Invalid username or password.
diff --git a/assets/getting-started.md.e767a449.lean.js b/assets/getting-started.md.8714bbcf.lean.js
similarity index 92%
rename from assets/getting-started.md.e767a449.lean.js
rename to assets/getting-started.md.8714bbcf.lean.js
index 08d7e92e..f19994cf 100644
--- a/assets/getting-started.md.e767a449.lean.js
+++ b/assets/getting-started.md.8714bbcf.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as n,d as o}from"./app.b4df1b52.js";const h=JSON.parse('{"title":"Git push results in \\"Authentication Failed”","description":"","frontmatter":{"title":"Git push results in \\"Authentication Failed”","author":"Anda Toshiki","date":"2023/2/21/ 10:54","editLink":true,"lastUpdated":true},"headers":[{"level":2,"title":"Issue","slug":"issue","link":"#issue","children":[]},{"level":2,"title":"Solution","slug":"solution","link":"#solution","children":[{"level":3,"title":"Solution 1","slug":"solution-1","link":"#solution-1","children":[]},{"level":3,"title":"Solution 2","slug":"solution-2","link":"#solution-2","children":[]}]}],"relativePath":"getting-started.md","lastUpdated":1679649941000}'),l={name:"getting-started.md"},e=o("",15),t=[e];function p(r,i,c,y,u,d){return n(),a("div",null,t)}const A=s(l,[["render",p]]);export{h as __pageData,A as default};
+import{_ as s,c as a,o as n,d as o}from"./app.b4df1b52.js";const h=JSON.parse('{"title":"Git push results in \\"Authentication Failed”","description":"","frontmatter":{"title":"Git push results in \\"Authentication Failed”","author":"Anda Toshiki","date":"2023/2/21/ 10:54","editLink":true,"lastUpdated":true},"headers":[{"level":2,"title":"Issue","slug":"issue","link":"#issue","children":[]},{"level":2,"title":"Solution","slug":"solution","link":"#solution","children":[{"level":3,"title":"Solution 1","slug":"solution-1","link":"#solution-1","children":[]},{"level":3,"title":"Solution 2","slug":"solution-2","link":"#solution-2","children":[]}]}],"relativePath":"getting-started.md","lastUpdated":1679745767000}'),l={name:"getting-started.md"},e=o("",15),t=[e];function p(r,i,c,y,u,d){return n(),a("div",null,t)}const A=s(l,[["render",p]]);export{h as __pageData,A as default};
diff --git a/assets/index.md.cb83f397.js b/assets/index.md.c6aabed9.js
similarity index 96%
rename from assets/index.md.cb83f397.js
rename to assets/index.md.c6aabed9.js
index 68247416..4295a4f8 100644
--- a/assets/index.md.cb83f397.js
+++ b/assets/index.md.c6aabed9.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a}from"./app.b4df1b52.js";const c=JSON.parse(`{"title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","description":"","frontmatter":{"layout":"home","title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","hero":{"name":"Toshiki's Notebook","text":"Research & Produce","tagline":"👨‍💻 Eternal & digital knowledge base for content craetion and notes management.","image":{"src":"/logos/logo.svg","alt":"Home logo"},"actions":[{"theme":"brand","text":"👉 Start Reading","link":"/getting-started"},{"theme":"alt","text":"🗒️ View on GitHub","link":"https://github.com/andatoshiki/toshiki-notebook"}]},"features":[{"icon":"🕒","title":"Tempus Fugit","details":"Tempus Fugit, which means \\"time flies\\" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential."},{"icon":"☕","title":"Carpe Diem","details":"Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning."},{"icon":"💡","title":"Epiphania","details":"An epiphany, derived from the Latin word \\"epiphania,\\" is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas."}]},"headers":[],"relativePath":"index.md","lastUpdated":1679649941000}`),i={name:"index.md"};function n(o,s,r,l,h,d){return a(),t("div")}const p=e(i,[["render",n]]);export{c as __pageData,p as default};
+import{_ as e,c as t,o as a}from"./app.b4df1b52.js";const c=JSON.parse(`{"title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","description":"","frontmatter":{"layout":"home","title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","hero":{"name":"Toshiki's Notebook","text":"Research & Produce","tagline":"👨‍💻 Eternal & digital knowledge base for content craetion and notes management.","image":{"src":"/logos/logo.svg","alt":"Home logo"},"actions":[{"theme":"brand","text":"👉 Start Reading","link":"/getting-started"},{"theme":"alt","text":"🗒️ View on GitHub","link":"https://github.com/andatoshiki/toshiki-notebook"}]},"features":[{"icon":"🕒","title":"Tempus Fugit","details":"Tempus Fugit, which means \\"time flies\\" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential."},{"icon":"☕","title":"Carpe Diem","details":"Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning."},{"icon":"💡","title":"Epiphania","details":"An epiphany, derived from the Latin word \\"epiphania,\\" is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas."}]},"headers":[],"relativePath":"index.md","lastUpdated":1679745767000}`),i={name:"index.md"};function n(o,s,r,l,h,d){return a(),t("div")}const p=e(i,[["render",n]]);export{c as __pageData,p as default};
diff --git a/assets/index.md.cb83f397.lean.js b/assets/index.md.c6aabed9.lean.js
similarity index 96%
rename from assets/index.md.cb83f397.lean.js
rename to assets/index.md.c6aabed9.lean.js
index 68247416..4295a4f8 100644
--- a/assets/index.md.cb83f397.lean.js
+++ b/assets/index.md.c6aabed9.lean.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a}from"./app.b4df1b52.js";const c=JSON.parse(`{"title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","description":"","frontmatter":{"layout":"home","title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","hero":{"name":"Toshiki's Notebook","text":"Research & Produce","tagline":"👨‍💻 Eternal & digital knowledge base for content craetion and notes management.","image":{"src":"/logos/logo.svg","alt":"Home logo"},"actions":[{"theme":"brand","text":"👉 Start Reading","link":"/getting-started"},{"theme":"alt","text":"🗒️ View on GitHub","link":"https://github.com/andatoshiki/toshiki-notebook"}]},"features":[{"icon":"🕒","title":"Tempus Fugit","details":"Tempus Fugit, which means \\"time flies\\" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential."},{"icon":"☕","title":"Carpe Diem","details":"Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning."},{"icon":"💡","title":"Epiphania","details":"An epiphany, derived from the Latin word \\"epiphania,\\" is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas."}]},"headers":[],"relativePath":"index.md","lastUpdated":1679649941000}`),i={name:"index.md"};function n(o,s,r,l,h,d){return a(),t("div")}const p=e(i,[["render",n]]);export{c as __pageData,p as default};
+import{_ as e,c as t,o as a}from"./app.b4df1b52.js";const c=JSON.parse(`{"title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","description":"","frontmatter":{"layout":"home","title":"Toshiki's Notebook","titleTemplate":"Eternal digital knowledge base for content craetion and notes management.","hero":{"name":"Toshiki's Notebook","text":"Research & Produce","tagline":"👨‍💻 Eternal & digital knowledge base for content craetion and notes management.","image":{"src":"/logos/logo.svg","alt":"Home logo"},"actions":[{"theme":"brand","text":"👉 Start Reading","link":"/getting-started"},{"theme":"alt","text":"🗒️ View on GitHub","link":"https://github.com/andatoshiki/toshiki-notebook"}]},"features":[{"icon":"🕒","title":"Tempus Fugit","details":"Tempus Fugit, which means \\"time flies\\" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential."},{"icon":"☕","title":"Carpe Diem","details":"Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning."},{"icon":"💡","title":"Epiphania","details":"An epiphany, derived from the Latin word \\"epiphania,\\" is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas."}]},"headers":[],"relativePath":"index.md","lastUpdated":1679745767000}`),i={name:"index.md"};function n(o,s,r,l,h,d){return a(),t("div")}const p=e(i,[["render",n]]);export{c as __pageData,p as default};
diff --git a/assets/javascript_notes_1_1-1.md.82d73735.js b/assets/javascript_notes_1_1-1.md.1269f243.js
similarity index 99%
rename from assets/javascript_notes_1_1-1.md.82d73735.js
rename to assets/javascript_notes_1_1-1.md.1269f243.js
index 0c1adc90..f5fb899c 100644
--- a/assets/javascript_notes_1_1-1.md.82d73735.js
+++ b/assets/javascript_notes_1_1-1.md.1269f243.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a as s,b as e,e as o,d as a,o as i,r as p}from"./app.b4df1b52.js";const T=JSON.parse('{"title":"1-1: Values","description":"Chapter 1-1 notes on values","frontmatter":{"title":"1-1: Values","description":"Chapter 1-1 notes on values"},"headers":[{"level":2,"title":"1-1-1: Numbers","slug":"_1-1-1-numbers","link":"#_1-1-1-numbers","children":[]},{"level":2,"title":"1-1-2: Arithmetic","slug":"_1-1-2-arithmetic","link":"#_1-1-2-arithmetic","children":[]},{"level":2,"title":"1-1-3: Strings","slug":"_1-1-3-strings","link":"#_1-1-3-strings","children":[{"level":3,"title":"1-1-3-FR: Further Reading","slug":"_1-1-3-fr-further-reading","link":"#_1-1-3-fr-further-reading","children":[]}]}],"relativePath":"javascript/notes/1/1-1.md","lastUpdated":1679649941000}'),r={name:"javascript/notes/1/1-1.md"},c=s("h1",{id:"_1-1-values",tabindex:"-1"},[e("1-1: Values "),s("a",{class:"header-anchor",href:"#_1-1-values","aria-hidden":"true"},"#")],-1),d={id:"_1-1-1-numbers",tabindex:"-1"},h=s("a",{class:"header-anchor",href:"#_1-1-1-numbers","aria-hidden":"true"},"#",-1),u=a(`
Values of the number type are numeric values, normally written as follows,
js
144
+import{_ as t,c as l,a as s,b as e,e as o,d as a,o as i,r as p}from"./app.b4df1b52.js";const T=JSON.parse('{"title":"1-1: Values","description":"Chapter 1-1 notes on values","frontmatter":{"title":"1-1: Values","description":"Chapter 1-1 notes on values"},"headers":[{"level":2,"title":"1-1-1: Numbers","slug":"_1-1-1-numbers","link":"#_1-1-1-numbers","children":[]},{"level":2,"title":"1-1-2: Arithmetic","slug":"_1-1-2-arithmetic","link":"#_1-1-2-arithmetic","children":[]},{"level":2,"title":"1-1-3: Strings","slug":"_1-1-3-strings","link":"#_1-1-3-strings","children":[{"level":3,"title":"1-1-3-FR: Further Reading","slug":"_1-1-3-fr-further-reading","link":"#_1-1-3-fr-further-reading","children":[]}]}],"relativePath":"javascript/notes/1/1-1.md","lastUpdated":1679745767000}'),r={name:"javascript/notes/1/1-1.md"},c=s("h1",{id:"_1-1-values",tabindex:"-1"},[e("1-1: Values "),s("a",{class:"header-anchor",href:"#_1-1-values","aria-hidden":"true"},"#")],-1),d={id:"_1-1-1-numbers",tabindex:"-1"},h=s("a",{class:"header-anchor",href:"#_1-1-1-numbers","aria-hidden":"true"},"#",-1),u=a(`
Values of the number type are numeric values, normally written as follows,
js
144
 
144
 
  • Put this into a program, it will cause the number 144 to come into existence inside the computer, with the following bash script, 144 might looks like this in bits,
    js
    0100000001100010000000000000000000000000000000000000000000000000
 
    0100000001100010000000000000000000000000000000000000000000000000
diff --git a/assets/javascript_notes_1_1-1.md.82d73735.lean.js b/assets/javascript_notes_1_1-1.md.1269f243.lean.js
similarity index 99%
rename from assets/javascript_notes_1_1-1.md.82d73735.lean.js
rename to assets/javascript_notes_1_1-1.md.1269f243.lean.js
index 93c8476b..18f61d01 100644
--- a/assets/javascript_notes_1_1-1.md.82d73735.lean.js
+++ b/assets/javascript_notes_1_1-1.md.1269f243.lean.js
@@ -1 +1 @@
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    Theme 
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diff --git a/assets/save_reading_outliers_1.md.bc528405.js b/assets/save_reading_outliers_1.md.457f7212.js
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    Introduction & Chapter 1: The Roseto Mystery 
    Summary: Introduction: The Roseto Mystery 
    Section 1. 
    In the late 1800s, immigrants from Roseto Valfortore, Italy, came to Pennsylvania to work in the slate quarry near the town of Bangor. The settlers established a new community, named after their old one: Roseto. They built schools, a park, small shops, and more than a dozen factories. They kept to themselves and did not interact much with the predominantly German and English populations of the towns around them.
    In the 1950s, a local doctor told Stewart Wolf, a medical researcher, that hardly anyone in Roseto under age sixty-five had heart disease. Wolf was curious. He did blood draws and EKG scans, and he analyzed physicians’ records and death certificates. Wolf was amazed that almost no one under fifty-five showed any signs of heart disease, which at the time was America’s leading cause of death in men under sixty-five. Wolf enlisted the help of John Bruhn, a sociologist. They found that there was no suicide, alcoholism, or drug addiction in Roseto: everyone seemed to be dying of old age. According to Gladwell, Roseto was an outlier.
    Section 2. 
    Wolf was forced to rule out diet and lifestyle as explanations, because the Rosetans had poor eating habits, smoked heavily, and were obese. He ruled out genetics after determining that Rosetans’ relatives in other parts of the country were not in comparably good health. Wolf eventually decided that what made Roseto’s inhabitants so healthy was the town itself—its culture and social structure. Many homes contained three generations living together, and with a population of just two thousand people, there were twenty-two separate civic organizations.
    Wolf and Bruhn were met with a great deal of skepticism. They had to work hard to convince the medical establishment that the values of where we live and the people around us have a significant impact on who we are. Gladwell wants Outliers to do for our understanding of success what Wolf did for our understanding of health.
    Summary: Chapter One: The Matthew Effect 
    Section 1. 
    Gladwell describes a game between two teams in the Canadian Hockey League, the most competitive junior hockey league in the world. Starting at a very young age, players are regularly assessed for talent, so that the best can be separated out and prepared for the next level. The system is designed to be a meritocracy.
    Section 2. 
    Gladwell wants to show that circumstances matter just as much for success as work ethic or intelligence. People often ask about the lifestyle, intelligence, or special talents of successful individuals, but not enough people ask when and where a person grew up. Gladwell likens people to trees: we all know that the tallest trees received the most sunlight, had nutrient-rich soil, and were lucky enough to avoid lumberjacks. He suggests that we study the environmental and social influences that make people successful.
    Section 3. 
    In the 1980s, Canadian psychologist Roger Barnsley observed that on elite Canadian hockey teams, whether youth league or NHL, a disproportionate number of players have birthdays in the first three months of the year.
    Section 4. 
    The explanation for the distribution of birthdays is simple: the cutoff date for an individual’s league assignment is January 1. A player born on January 2 will be 12 months older than one born at the end of December. At the age of nine or ten, this often translates into a huge difference in size, coordination, and maturity. By age ten, coaches regularly pick the oldest and largest potential players for the more competitive “rep squads,” where the players will receive better coaching, have more practice time, and play many more games. By thirteen or fourteen, all of the extra experience and coaching will have actually made the players better, and they will be selected for the more competitive league(s). The same thing happens in American youth baseball and European soccer, but with different cutoff dates.
    The phenomenon is also observable in education. Economists Kelly Bedard and Elizabeth Dhuey found that on math and science tests, the older children in fourth grade regularly score better than the youngest children. This can affect whether a child qualifies for a gifted program. When Bedard and Dhuey extended their analysis to four-year colleges, they found that the students who belonged to the relatively youngest group were underrepresented by more than 10 percent.
    Section 5. 
    The top-level hockey players were given opportunities they neither deserved nor earned. Sociologist Robert Merton called this the “Matthew Effect,” after the verse in the Gospel of Matthew:
    “For unto everyone that hath shall be given, and he shall have abundance. But from that hath not shall be taken away even that which he hath.”
    The successful receive more resources: the best students receive the best teaching, the richest citizens get the biggest tax breaks, the largest kids get the best coaching. Sociologists call this “accumulative advantage.” Gladwell points out that cutoff dates exclude nearly half of the potential athletes from a population. Junior hockey teams in the Czech Republic show the same unbalanced distribution of birthdays as in Canada. If Canada or the Czech Republic separated each of their youth leagues into two separate leagues, one for kids born in the first half of the year, and one for kids born in the second half of the year, they would have twice as many athletes available for their national teams. Similarly, schools could separate kindergarten classes into students born in the first, middle, and last four months of the year. The benefits would justify the added administrative work, but, writes Gladwell, the scheme would run afoul of society’s need to believe that individual merit matters more than the rules society has created.
    Section 6. 
    Gord Wasden, the father of one of the Canadian Hockey League boys from the first section, describes his son. Scott Wasden worked hard to get where he is, but he has also generally had the advantage of being big compared to others on his team. He was born on January 4.
    Analysis: Introduction: The Roseto Mystery & Chapter 1: The Matthew Effect 
    Gladwell's thesis argues that that the idea of rugged, individual success is not accurate. Rather, the most successful person doesn’t thrive without some environmental and social influence plus a dose of good fortune.  After laying out the concepts of a meritocracy and suggesting that this is the way that hockey players advance in Canada, he immediately undercuts this idea. Gladwell uses the illustration of birthday distribution as an example of an invisible contributor to the success of hockey players. With a registration cutoff date of January 1, players born from January 2 through March 31 are older than teammates born later in the year. These older players are likely bigger, faster, more coordinated, and more mature. Since the older players are seen as more skilled, they get selected for more advanced leagues with more practice, more games, and higher-quality coaching. By the time these older players reach their early teens, the extra advantages gained from being judged better because of their birthday translate into being better players. Similarly, the age cutoff for school registrations often mistakes maturity for ability. As a result, the older children appear smarter, get put into advanced groups, and qualify for gifted programs. The birthdate bias carries through to college.
    Advantages result in more advantages. Gladwell reinforces this idea with the “Matthew Effect,” which states that "success leads to more success." More simply: by being a little bit better, a hockey player will get opportunities that may result in the player becoming an outlier. Gladwell implies that the systems that determine success are not efficient. He asks readers to question the way we, as a society, think about success. He suggests that changing the systems in athletics and education would chip away at the myth of individual merit as the chief marker of success and help level the playing field. Gladwell's model for this phenomenon is hockey player Scott Wasden. By demonstrating that Scott had the passion, talent, and work ethic for the game, as well as the good luck to be born on January 4, Gladwell reasons that Wasden, like many others he will be profiling, benefit by being both good and lucky.
    Reference
    ',28),i=[n];function r(h,l,d,c,u,m){return a(),t("div",null,i)}const p=e(s,[["render",r]]);export{y as __pageData,p as default};
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    Introduction & Chapter 1: The Roseto Mystery 
    Summary: Introduction: The Roseto Mystery 
    Section 1. 
    In the late 1800s, immigrants from Roseto Valfortore, Italy, came to Pennsylvania to work in the slate quarry near the town of Bangor. The settlers established a new community, named after their old one: Roseto. They built schools, a park, small shops, and more than a dozen factories. They kept to themselves and did not interact much with the predominantly German and English populations of the towns around them.
    In the 1950s, a local doctor told Stewart Wolf, a medical researcher, that hardly anyone in Roseto under age sixty-five had heart disease. Wolf was curious. He did blood draws and EKG scans, and he analyzed physicians’ records and death certificates. Wolf was amazed that almost no one under fifty-five showed any signs of heart disease, which at the time was America’s leading cause of death in men under sixty-five. Wolf enlisted the help of John Bruhn, a sociologist. They found that there was no suicide, alcoholism, or drug addiction in Roseto: everyone seemed to be dying of old age. According to Gladwell, Roseto was an outlier.
    Section 2. 
    Wolf was forced to rule out diet and lifestyle as explanations, because the Rosetans had poor eating habits, smoked heavily, and were obese. He ruled out genetics after determining that Rosetans’ relatives in other parts of the country were not in comparably good health. Wolf eventually decided that what made Roseto’s inhabitants so healthy was the town itself—its culture and social structure. Many homes contained three generations living together, and with a population of just two thousand people, there were twenty-two separate civic organizations.
    Wolf and Bruhn were met with a great deal of skepticism. They had to work hard to convince the medical establishment that the values of where we live and the people around us have a significant impact on who we are. Gladwell wants Outliers to do for our understanding of success what Wolf did for our understanding of health.
    Summary: Chapter One: The Matthew Effect 
    Section 1. 
    Gladwell describes a game between two teams in the Canadian Hockey League, the most competitive junior hockey league in the world. Starting at a very young age, players are regularly assessed for talent, so that the best can be separated out and prepared for the next level. The system is designed to be a meritocracy.
    Section 2. 
    Gladwell wants to show that circumstances matter just as much for success as work ethic or intelligence. People often ask about the lifestyle, intelligence, or special talents of successful individuals, but not enough people ask when and where a person grew up. Gladwell likens people to trees: we all know that the tallest trees received the most sunlight, had nutrient-rich soil, and were lucky enough to avoid lumberjacks. He suggests that we study the environmental and social influences that make people successful.
    Section 3. 
    In the 1980s, Canadian psychologist Roger Barnsley observed that on elite Canadian hockey teams, whether youth league or NHL, a disproportionate number of players have birthdays in the first three months of the year.
    Section 4. 
    The explanation for the distribution of birthdays is simple: the cutoff date for an individual’s league assignment is January 1. A player born on January 2 will be 12 months older than one born at the end of December. At the age of nine or ten, this often translates into a huge difference in size, coordination, and maturity. By age ten, coaches regularly pick the oldest and largest potential players for the more competitive “rep squads,” where the players will receive better coaching, have more practice time, and play many more games. By thirteen or fourteen, all of the extra experience and coaching will have actually made the players better, and they will be selected for the more competitive league(s). The same thing happens in American youth baseball and European soccer, but with different cutoff dates.
    The phenomenon is also observable in education. Economists Kelly Bedard and Elizabeth Dhuey found that on math and science tests, the older children in fourth grade regularly score better than the youngest children. This can affect whether a child qualifies for a gifted program. When Bedard and Dhuey extended their analysis to four-year colleges, they found that the students who belonged to the relatively youngest group were underrepresented by more than 10 percent.
    Section 5. 
    The top-level hockey players were given opportunities they neither deserved nor earned. Sociologist Robert Merton called this the “Matthew Effect,” after the verse in the Gospel of Matthew:
    “For unto everyone that hath shall be given, and he shall have abundance. But from that hath not shall be taken away even that which he hath.”
    The successful receive more resources: the best students receive the best teaching, the richest citizens get the biggest tax breaks, the largest kids get the best coaching. Sociologists call this “accumulative advantage.” Gladwell points out that cutoff dates exclude nearly half of the potential athletes from a population. Junior hockey teams in the Czech Republic show the same unbalanced distribution of birthdays as in Canada. If Canada or the Czech Republic separated each of their youth leagues into two separate leagues, one for kids born in the first half of the year, and one for kids born in the second half of the year, they would have twice as many athletes available for their national teams. Similarly, schools could separate kindergarten classes into students born in the first, middle, and last four months of the year. The benefits would justify the added administrative work, but, writes Gladwell, the scheme would run afoul of society’s need to believe that individual merit matters more than the rules society has created.
    Section 6. 
    Gord Wasden, the father of one of the Canadian Hockey League boys from the first section, describes his son. Scott Wasden worked hard to get where he is, but he has also generally had the advantage of being big compared to others on his team. He was born on January 4.
    Analysis: Introduction: The Roseto Mystery & Chapter 1: The Matthew Effect 
    Gladwell's thesis argues that that the idea of rugged, individual success is not accurate. Rather, the most successful person doesn’t thrive without some environmental and social influence plus a dose of good fortune.  After laying out the concepts of a meritocracy and suggesting that this is the way that hockey players advance in Canada, he immediately undercuts this idea. Gladwell uses the illustration of birthday distribution as an example of an invisible contributor to the success of hockey players. With a registration cutoff date of January 1, players born from January 2 through March 31 are older than teammates born later in the year. These older players are likely bigger, faster, more coordinated, and more mature. Since the older players are seen as more skilled, they get selected for more advanced leagues with more practice, more games, and higher-quality coaching. By the time these older players reach their early teens, the extra advantages gained from being judged better because of their birthday translate into being better players. Similarly, the age cutoff for school registrations often mistakes maturity for ability. As a result, the older children appear smarter, get put into advanced groups, and qualify for gifted programs. The birthdate bias carries through to college.
    Advantages result in more advantages. Gladwell reinforces this idea with the “Matthew Effect,” which states that "success leads to more success." More simply: by being a little bit better, a hockey player will get opportunities that may result in the player becoming an outlier. Gladwell implies that the systems that determine success are not efficient. He asks readers to question the way we, as a society, think about success. He suggests that changing the systems in athletics and education would chip away at the myth of individual merit as the chief marker of success and help level the playing field. Gladwell's model for this phenomenon is hockey player Scott Wasden. By demonstrating that Scott had the passion, talent, and work ethic for the game, as well as the good luck to be born on January 4, Gladwell reasons that Wasden, like many others he will be profiling, benefit by being both good and lucky.
    Reference
    ',28),i=[n];function r(h,l,d,c,u,m){return a(),t("div",null,i)}const p=e(s,[["render",r]]);export{y as __pageData,p as default};
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-import{_ as e,c as t,o as a,d as o}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes","frontmatter":{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Two: The 10,000-Hour Rule","slug":"summary-chapter-two-the-10-000-hour-rule","link":"#summary-chapter-two-the-10-000-hour-rule","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Two: The 10,000-Hour Rule","slug":"analysis-chapter-two-the-10-000-hour-rule","link":"#analysis-chapter-two-the-10-000-hour-rule","children":[]}],"relativePath":"save/reading/outliers/2.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/2.md"},n=o('
    Chapter Two: The 10,000-Hour Rule 
    Summary: Chapter Two: The 10,000-Hour Rule 
    Section 1. 
    Bill Joy, a co-founder of Sun Microsystems, is one of the most influential computer programmers of all time. Joy attended the University of Michigan, thinking to become a biologist or mathematician, but he became obsessed with the Computer Center that opened during his freshman year. In 1975, he enrolled in graduate school at UC Berkeley. At both schools, Bill Joy spent much of his free time programming. After graduating from Berkeley, he founded Sun Microsystems, eventually rewriting the Java programming language. He would appear to be a good example of success based on individual merit.
    Section 2. 
    If achievement is the combination of talent and preparation, how much does innate talent affect one’s success? In the 1990s, a study at Berlin’s elite Academy of Music determined that, regardless of instrument, all of the world-class students had practiced more than 10,000 hours. They did not find anyone at the top level who spent less time, nor did they find anyone who spent that amount of time who was not successful. Neurologist Daniel Levitin states that, across many fields, world-class expertise is never accomplished in less than 10,000 hours. The law holds even for a prodigy like Mozart, who started composing at age six: he did not compose his first masterwork until he was twenty-one. The youth athletes from the previous chapter who made it to the professional level put in 10,000 hours of practice. And note: individuals cannot normally put in that much practice without help. Most people will need supportive parents, financial stability, and probably a special program—like an all-star youth hockey team.
    Section 3. 
    Bill Joy was certainly intelligent, having achieved a perfect score on the math portion of his Scholastic Aptitude Test. His opportunities, however, were extraordinary. Bill Joy happened to choose a college that had a time-sharing computer available, something that was exceedingly rare during the early 1970s. While most students had to pay for computer time, Bill Joy exploited a bug in the college’s system to gain unlimited access to the Computer Center, which was walking distance from where he lived. He was able to spend almost all of his free time programming, and when he went to Berkeley, he had a terminal at home, where he could program until he fell asleep at his keyboard. Bill Joy was able to accumulate 10,000 hours while in college.
    Section 4. 
    The Beatles are another example of the 10,000-hours principle. In 1960, when they were still a high school rock band, they were given the chance to travel to Hamburg, Germany and play in various strip clubs. The Beatles were contracted to play for hours every night, seven nights a week, and thereby were forced to develop as musicians. After a year and a half, they had performed 270 nights. By 1964, when they first found commercial success, they had performed an estimated twelve hundred times—more than most band bands do in an entire career.
    Section 5. 
    Born in Seattle to affluent parents, Bill Gates was sent to a private school for seventh grade. The school’s Mother’s Club funded the purchase of a time-sharing terminal connected to a mainframe computer in Seattle. As an eighth-grader, Gates was able to start programming. When the Mother’s Club could no longer pay for computing time, Gates was able to continue programming at Information Sciences, Inc. (ISI) through a connection he made with one of the school parents. After that, one of ISI’s founders recommended Gates for a programming project at the Bonneville Power station. Gates was able to leave high school during his senior year to program for the Bonneville Power station as an independent study project. By the time Bill Gates dropped out of Harvard, he was well past 10,000 hours of experience.
    Section 6. 
    In a list of the seventy-five richest people in human history, going as far back as ancient Egypt and converting all wealth estimates into modern U.S. dollars, fourteen names are Americans born within nine years of one another (including John D. Rockefeller and J.P. Morgan). What accounts for the fact that a list that covers thousands of years should have 20 percent of its members so close together? The fourteen Americans happened to live during the 1860s and 1870s, when the American economy was undergoing a huge transformation: the expansion of the railroads and the creation of Wall Street. Gladwell argues that the fourteen names are so close in birth date because they were all the perfect age to seize the opportunities available.
    Bill Joy and Bill Gates were also born at just the right time. In 1975, Popular Electronics ran a cover story about the Altair 8800, a $397 microcomputer kit. Someone born before 1954 would likely already have a job with IBM, working on mainframes. Someone born after 1956 would likely still be in high school. Most of the biggest pioneers in the modern computer industry, including Bill Gates, Bill Joy, Steve Jobs, and Eric Schmidt, were born in 1954 or 1955, as were Joy’s three fellow founders at Sun.
    Analysis: Chapter Two: The 10,000-Hour Rule 
    Gladwell introduces his controversial and widely disputed 10,000 hours rule. Simply put, the rule suggests that to master a skill, an individual needs to practice it for 10,000 hours. Gladwell argues that, like hockey, success in computing requires both skill and luck, rather than pure, simple, natural ability. Gladwell's example is situated at the University of Michigan, specifically the new computer center, in 1971. The story of Bill Joy undermines the idea of success as an inexplicable, miraculous accomplishment. Though Gladwell agrees Joy is bright and talented, Joy also lucks into several happy accidents that allow for increased access. These strokes of luck give Joy the opportunity to become a computer expert. Gladwell's use of a psychological study conducted at the Academy of Music in Berlin, Germany, in the early 1990s forms the crux of his argument in this chapter. However, critics have suggested that this study was flawed and that there is no incontrovertible evidence to suggest that doing anything for 10,000 hours guarantees mastery. Rather, practice is, as Gladwell points out elsewhere throughout the text, just one of the factors in success. However, he also correlates the familial and economic advantages necessary to reach 10,000 of practice time, reinforcing the larger thesis of the book.
    Gladwell argues that the Beatles and Bill Gates are examples of his notion of time spent directly relating to mastery. While detailing how the Beatles reached the 10,000-hour threshold for mastery, Gladwell also highlights the lucky breaks they had in achieving success, like the connection that landed the band in Hamburg’s music scene. Additionally, while Gates has become something of an American folk hero, Gladwell argues that Gates did not reach his great achievements completely on his own. His wealthy family, his lucky interaction with a computer in 1968, and his college experience allowed him far greater access to opportunity. Without this combination of factors, along with his intelligence and drive, Gates would likely not have become a household name. Again, Gladwell reinforces the idea that success comes not only from being good, but from having no small amount of luck, whether that be time, money, or, in an echo of the hockey player example, birthdate.
    Gladwell claims that one important factor of success is the year in which one is born. In terms of wealth, there are 14 Americans, born in a nine-year period of the 1800s, who are among the richest people in history. This suggests that there was some connection to when they were born and the opportunities available to them in terms of innovation and invention, as well as the position they were in to take advantage of the opportunities. Similarly, men born in the same era of Bill Gates were coming of age at the bleeding edge of technology. Proximity to social and technological change, as well as the wealth and connections to take advantage of it, put these men in an advantageous position. Being in the right place at the right time, Gladwell argues, has at least as much to do with success as one's inborn abilities.
    Reference
    ',20),r=[n];function s(h,l,c,d,u,m){return a(),t("div",null,r)}const g=e(i,[["render",s]]);export{f as __pageData,g as default};
+import{_ as e,c as t,o as a,d as o}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes","frontmatter":{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Two: The 10,000-Hour Rule","slug":"summary-chapter-two-the-10-000-hour-rule","link":"#summary-chapter-two-the-10-000-hour-rule","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Two: The 10,000-Hour Rule","slug":"analysis-chapter-two-the-10-000-hour-rule","link":"#analysis-chapter-two-the-10-000-hour-rule","children":[]}],"relativePath":"save/reading/outliers/2.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/2.md"},n=o('
    Chapter Two: The 10,000-Hour Rule 
    Summary: Chapter Two: The 10,000-Hour Rule 
    Section 1. 
    Bill Joy, a co-founder of Sun Microsystems, is one of the most influential computer programmers of all time. Joy attended the University of Michigan, thinking to become a biologist or mathematician, but he became obsessed with the Computer Center that opened during his freshman year. In 1975, he enrolled in graduate school at UC Berkeley. At both schools, Bill Joy spent much of his free time programming. After graduating from Berkeley, he founded Sun Microsystems, eventually rewriting the Java programming language. He would appear to be a good example of success based on individual merit.
    Section 2. 
    If achievement is the combination of talent and preparation, how much does innate talent affect one’s success? In the 1990s, a study at Berlin’s elite Academy of Music determined that, regardless of instrument, all of the world-class students had practiced more than 10,000 hours. They did not find anyone at the top level who spent less time, nor did they find anyone who spent that amount of time who was not successful. Neurologist Daniel Levitin states that, across many fields, world-class expertise is never accomplished in less than 10,000 hours. The law holds even for a prodigy like Mozart, who started composing at age six: he did not compose his first masterwork until he was twenty-one. The youth athletes from the previous chapter who made it to the professional level put in 10,000 hours of practice. And note: individuals cannot normally put in that much practice without help. Most people will need supportive parents, financial stability, and probably a special program—like an all-star youth hockey team.
    Section 3. 
    Bill Joy was certainly intelligent, having achieved a perfect score on the math portion of his Scholastic Aptitude Test. His opportunities, however, were extraordinary. Bill Joy happened to choose a college that had a time-sharing computer available, something that was exceedingly rare during the early 1970s. While most students had to pay for computer time, Bill Joy exploited a bug in the college’s system to gain unlimited access to the Computer Center, which was walking distance from where he lived. He was able to spend almost all of his free time programming, and when he went to Berkeley, he had a terminal at home, where he could program until he fell asleep at his keyboard. Bill Joy was able to accumulate 10,000 hours while in college.
    Section 4. 
    The Beatles are another example of the 10,000-hours principle. In 1960, when they were still a high school rock band, they were given the chance to travel to Hamburg, Germany and play in various strip clubs. The Beatles were contracted to play for hours every night, seven nights a week, and thereby were forced to develop as musicians. After a year and a half, they had performed 270 nights. By 1964, when they first found commercial success, they had performed an estimated twelve hundred times—more than most band bands do in an entire career.
    Section 5. 
    Born in Seattle to affluent parents, Bill Gates was sent to a private school for seventh grade. The school’s Mother’s Club funded the purchase of a time-sharing terminal connected to a mainframe computer in Seattle. As an eighth-grader, Gates was able to start programming. When the Mother’s Club could no longer pay for computing time, Gates was able to continue programming at Information Sciences, Inc. (ISI) through a connection he made with one of the school parents. After that, one of ISI’s founders recommended Gates for a programming project at the Bonneville Power station. Gates was able to leave high school during his senior year to program for the Bonneville Power station as an independent study project. By the time Bill Gates dropped out of Harvard, he was well past 10,000 hours of experience.
    Section 6. 
    In a list of the seventy-five richest people in human history, going as far back as ancient Egypt and converting all wealth estimates into modern U.S. dollars, fourteen names are Americans born within nine years of one another (including John D. Rockefeller and J.P. Morgan). What accounts for the fact that a list that covers thousands of years should have 20 percent of its members so close together? The fourteen Americans happened to live during the 1860s and 1870s, when the American economy was undergoing a huge transformation: the expansion of the railroads and the creation of Wall Street. Gladwell argues that the fourteen names are so close in birth date because they were all the perfect age to seize the opportunities available.
    Bill Joy and Bill Gates were also born at just the right time. In 1975, Popular Electronics ran a cover story about the Altair 8800, a $397 microcomputer kit. Someone born before 1954 would likely already have a job with IBM, working on mainframes. Someone born after 1956 would likely still be in high school. Most of the biggest pioneers in the modern computer industry, including Bill Gates, Bill Joy, Steve Jobs, and Eric Schmidt, were born in 1954 or 1955, as were Joy’s three fellow founders at Sun.
    Analysis: Chapter Two: The 10,000-Hour Rule 
    Gladwell introduces his controversial and widely disputed 10,000 hours rule. Simply put, the rule suggests that to master a skill, an individual needs to practice it for 10,000 hours. Gladwell argues that, like hockey, success in computing requires both skill and luck, rather than pure, simple, natural ability. Gladwell's example is situated at the University of Michigan, specifically the new computer center, in 1971. The story of Bill Joy undermines the idea of success as an inexplicable, miraculous accomplishment. Though Gladwell agrees Joy is bright and talented, Joy also lucks into several happy accidents that allow for increased access. These strokes of luck give Joy the opportunity to become a computer expert. Gladwell's use of a psychological study conducted at the Academy of Music in Berlin, Germany, in the early 1990s forms the crux of his argument in this chapter. However, critics have suggested that this study was flawed and that there is no incontrovertible evidence to suggest that doing anything for 10,000 hours guarantees mastery. Rather, practice is, as Gladwell points out elsewhere throughout the text, just one of the factors in success. However, he also correlates the familial and economic advantages necessary to reach 10,000 of practice time, reinforcing the larger thesis of the book.
    Gladwell argues that the Beatles and Bill Gates are examples of his notion of time spent directly relating to mastery. While detailing how the Beatles reached the 10,000-hour threshold for mastery, Gladwell also highlights the lucky breaks they had in achieving success, like the connection that landed the band in Hamburg’s music scene. Additionally, while Gates has become something of an American folk hero, Gladwell argues that Gates did not reach his great achievements completely on his own. His wealthy family, his lucky interaction with a computer in 1968, and his college experience allowed him far greater access to opportunity. Without this combination of factors, along with his intelligence and drive, Gates would likely not have become a household name. Again, Gladwell reinforces the idea that success comes not only from being good, but from having no small amount of luck, whether that be time, money, or, in an echo of the hockey player example, birthdate.
    Gladwell claims that one important factor of success is the year in which one is born. In terms of wealth, there are 14 Americans, born in a nine-year period of the 1800s, who are among the richest people in history. This suggests that there was some connection to when they were born and the opportunities available to them in terms of innovation and invention, as well as the position they were in to take advantage of the opportunities. Similarly, men born in the same era of Bill Gates were coming of age at the bleeding edge of technology. Proximity to social and technological change, as well as the wealth and connections to take advantage of it, put these men in an advantageous position. Being in the right place at the right time, Gladwell argues, has at least as much to do with success as one's inborn abilities.
    Reference
    ',20),r=[n];function s(h,l,c,d,u,m){return a(),t("div",null,r)}const g=e(i,[["render",s]]);export{f as __pageData,g as default};
diff --git a/assets/save_reading_outliers_2.md.93d4b0ec.lean.js b/assets/save_reading_outliers_2.md.57cc24bd.lean.js
similarity index 95%
rename from assets/save_reading_outliers_2.md.93d4b0ec.lean.js
rename to assets/save_reading_outliers_2.md.57cc24bd.lean.js
index 533af065..29404b8c 100644
--- a/assets/save_reading_outliers_2.md.93d4b0ec.lean.js
+++ b/assets/save_reading_outliers_2.md.57cc24bd.lean.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,d as o}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes","frontmatter":{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Two: The 10,000-Hour Rule","slug":"summary-chapter-two-the-10-000-hour-rule","link":"#summary-chapter-two-the-10-000-hour-rule","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Two: The 10,000-Hour Rule","slug":"analysis-chapter-two-the-10-000-hour-rule","link":"#analysis-chapter-two-the-10-000-hour-rule","children":[]}],"relativePath":"save/reading/outliers/2.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/2.md"},n=o("",20),r=[n];function s(h,l,c,d,u,m){return a(),t("div",null,r)}const g=e(i,[["render",s]]);export{f as __pageData,g as default};
+import{_ as e,c as t,o as a,d as o}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes","frontmatter":{"title":"Chapter Two: The 10,000-Hour Rule","description":"Summary of Chapter Two: The 10,000-Hour Rule of Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Two: The 10,000-Hour Rule","slug":"summary-chapter-two-the-10-000-hour-rule","link":"#summary-chapter-two-the-10-000-hour-rule","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Two: The 10,000-Hour Rule","slug":"analysis-chapter-two-the-10-000-hour-rule","link":"#analysis-chapter-two-the-10-000-hour-rule","children":[]}],"relativePath":"save/reading/outliers/2.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/2.md"},n=o("",20),r=[n];function s(h,l,c,d,u,m){return a(),t("div",null,r)}const g=e(i,[["render",s]]);export{f as __pageData,g as default};
diff --git a/assets/save_reading_outliers_3.md.20bd5446.js b/assets/save_reading_outliers_3.md.e3dda0fb.js
similarity index 99%
rename from assets/save_reading_outliers_3.md.20bd5446.js
rename to assets/save_reading_outliers_3.md.e3dda0fb.js
index a9cafe78..639d9547 100644
--- a/assets/save_reading_outliers_3.md.20bd5446.js
+++ b/assets/save_reading_outliers_3.md.e3dda0fb.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,d as s}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Three: The Trouble with Geniuses, Part 1","slug":"summary-chapter-three-the-trouble-with-geniuses-part-1","link":"#summary-chapter-three-the-trouble-with-geniuses-part-1","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]}]},{"level":2,"title":"Analysis: Chapter Three: The Trouble with Geniuses, Part 1","slug":"analysis-chapter-three-the-trouble-with-geniuses-part-1","link":"#analysis-chapter-three-the-trouble-with-geniuses-part-1","children":[]}],"relativePath":"save/reading/outliers/3.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/3.md"},n=s('
    Chapter 3: The Trouble with Geniuses, Part 1 
    Summary: Chapter Three: The Trouble with Geniuses, Part 1 
    Section 1. 
    Chris Langan appeared on the television trivia show 1 vs. 100 after being the subject of interviews and at least one documentary, due to his extremely high IQ. He had little difficulty in high school, got a perfect score on his SAT, and read through Principia Mathematica as a teenager. On 1 vs. 100, Langan cashed out with winnings of $250,000.
    Section 2. 
    Shortly after World War I, Lewis Terman, creator of the widely used Stanford-Binet IQ test, became fascinated with child prodigies. In 1921, he identified exceptionally gifted 1,470 students who came to be known as the “Termites.” Terman kept track of them over the years, carefully cataloging their educational achievement, marriages, psychological health, and employment. Terman was sure that the Termites would be the future elite of the United States. The same confidence underlies the use of IQ-like tests, such as the SAT, to assess applicants at Ivy League schools and corporations such as Microsoft and Google. Gladwell states that Terman was wrong about the Termites, and if he had met Chris Langan as a teenager, he would have been wrong about him, too.
    Section 3. 
    Gladwell gives two examples—one easy and one much harder—of questions that use visual puzzles to test IQ, without requiring any language abilities or specific factual knowledge. The average human will score 100. Those scoring below 70 are considered mentally disabled, and those who are successful in graduate programs likely have an IQ of 115 or higher. According to Gladwell, however, above 120 IQ makes little or no difference to success. A similar point applies to basketball: height is certainly an advantage, but there is, at best, modest value in being six foot seven instead of six foot six. A basketball player just needs to be tall enough.
    A list of the last twenty-five Americans to win a Nobel Prize in Medicine includes graduates of prestigious schools, such as Columbia, Harvard, and MIT, but also graduates of DePauw, Holy Cross, and Gettysburg College. Similarly, there have been American Nobel laureates in Chemistry from Harvard and MIT, but also from Notre Dame and the University of Illinois. Harvard might have more intelligent students, but many other colleges have students smart enough to win a Nobel.
    At the University of Michigan law school, around 10 percent of students are racial minorities. Without affirmative action, there would be less than 3 percent. Looking at career performance after graduation, Michigan found no difference between white and minority graduates. Minority students come into law school with weaker academic credentials than their white counterparts, but they are above the threshold required to be just as successful.
    Section 4. 
    Not all questions that test for intelligence have a single correct answer. A different sort of question might ask for a list of different uses for a brick, or a blanket. A question like this measures imagination and creativity. At a top British high school, one student lists more than ten uses, many of which are comical. Another student, a prodigy with one of the school’s highest IQs, lists just a few uses, all of which are practical. Compared to an IQ test, asking about different uses for a brick might be a better way to identify future Nobel Prize winners.
    Section 5. 
    Terman’s error was using intelligence alone to choose his Termites. While some of the Termites had successful careers, an unexpectedly high went on to careers that even Terman didn’t consider to be successful. The two students tested by Terman’s team who actually did go on to win Nobels were not selected as Termites: their IQs were too low. Terman eventually concluded that “intellect and achievement are far from perfectly correlated.”
    Gladwell states that to understand Chris Langan’s prospects of becoming a “true outlier,” one must learn more about him.
    Analysis: Chapter Three: The Trouble with Geniuses, Part 1 
    Intelligence, Gladwell argues, does not equal success. He dedicates this chapter to the examination of geniuses. Comparing the young subjects of Lewis Terman to Chris Langan, Gladwell argues against Terman’s idea that genius is a key to societal advancement. Gladwell lists Langan’s early accomplishments as a shining example of Terman's idea, then swiftly undercuts expectations. Gladwell argues again that individuals do not succeed or fail solely on their own, but rather due to a constellation of factors, many of which are uncontrollable. Langan's early achievements would suggest great things and a continued path toward accomplishment, but Gladwell includes the anecdote of his game show appearance to undermine the notion that genius equals success. Using two questions from an IQ test, Gladwell introduces the idea of an IQ threshold to examine the the larger notion of intelligence and its limitations. Arguing that the measure of someone’s intelligence is only helpful up to a point, Gladwell uses examples of schools that Nobel laureates attended for undergraduate studies. Some, he points out, are elite institutions; others are not. Additionally, he points to success among graduates of the law school at the University of Michigan. There was no quantifiable difference in success post-graduation between white and POC students, some of whom were admitted under affirmative action with slightly lower undergraduate grades and standardized test scores. Reasonably, then, the level of intelligence beyond a certain point is moot. All of the students were intelligent enough to graduate, and beyond that, he argues, their intelligence predicted nothing.
    Elements other than intelligence must contribute to success. Gladwell expands on his notion of an intelligence threshold and examines these other factors through an example of a question on a divergence test. Using examples of two students at an elite British school, Gladwell shows that the divergence test has no right answers, but instead looks for answers that demonstrate uniqueness and creativity. Intelligence matters, but so does imagination, creativity, and outside-the-box thinking. Gladwell circles back to Terman, reinforcing that the error when choosing his Termites was a focus on intelligence alone. He once again turns his attention to Chris Langan, foreshadowing that Langan’s story did not follow a direct line to achievement. Intelligence alone does not offer a certain path to success.
    Reference
    ',19),o=[n];function r(l,h,c,d,u,m){return a(),t("div",null,o)}const p=e(i,[["render",r]]);export{f as __pageData,p as default};
+import{_ as e,c as t,o as a,d as s}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Three: The Trouble with Geniuses, Part 1","slug":"summary-chapter-three-the-trouble-with-geniuses-part-1","link":"#summary-chapter-three-the-trouble-with-geniuses-part-1","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]}]},{"level":2,"title":"Analysis: Chapter Three: The Trouble with Geniuses, Part 1","slug":"analysis-chapter-three-the-trouble-with-geniuses-part-1","link":"#analysis-chapter-three-the-trouble-with-geniuses-part-1","children":[]}],"relativePath":"save/reading/outliers/3.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/3.md"},n=s('
    Chapter 3: The Trouble with Geniuses, Part 1 
    Summary: Chapter Three: The Trouble with Geniuses, Part 1 
    Section 1. 
    Chris Langan appeared on the television trivia show 1 vs. 100 after being the subject of interviews and at least one documentary, due to his extremely high IQ. He had little difficulty in high school, got a perfect score on his SAT, and read through Principia Mathematica as a teenager. On 1 vs. 100, Langan cashed out with winnings of $250,000.
    Section 2. 
    Shortly after World War I, Lewis Terman, creator of the widely used Stanford-Binet IQ test, became fascinated with child prodigies. In 1921, he identified exceptionally gifted 1,470 students who came to be known as the “Termites.” Terman kept track of them over the years, carefully cataloging their educational achievement, marriages, psychological health, and employment. Terman was sure that the Termites would be the future elite of the United States. The same confidence underlies the use of IQ-like tests, such as the SAT, to assess applicants at Ivy League schools and corporations such as Microsoft and Google. Gladwell states that Terman was wrong about the Termites, and if he had met Chris Langan as a teenager, he would have been wrong about him, too.
    Section 3. 
    Gladwell gives two examples—one easy and one much harder—of questions that use visual puzzles to test IQ, without requiring any language abilities or specific factual knowledge. The average human will score 100. Those scoring below 70 are considered mentally disabled, and those who are successful in graduate programs likely have an IQ of 115 or higher. According to Gladwell, however, above 120 IQ makes little or no difference to success. A similar point applies to basketball: height is certainly an advantage, but there is, at best, modest value in being six foot seven instead of six foot six. A basketball player just needs to be tall enough.
    A list of the last twenty-five Americans to win a Nobel Prize in Medicine includes graduates of prestigious schools, such as Columbia, Harvard, and MIT, but also graduates of DePauw, Holy Cross, and Gettysburg College. Similarly, there have been American Nobel laureates in Chemistry from Harvard and MIT, but also from Notre Dame and the University of Illinois. Harvard might have more intelligent students, but many other colleges have students smart enough to win a Nobel.
    At the University of Michigan law school, around 10 percent of students are racial minorities. Without affirmative action, there would be less than 3 percent. Looking at career performance after graduation, Michigan found no difference between white and minority graduates. Minority students come into law school with weaker academic credentials than their white counterparts, but they are above the threshold required to be just as successful.
    Section 4. 
    Not all questions that test for intelligence have a single correct answer. A different sort of question might ask for a list of different uses for a brick, or a blanket. A question like this measures imagination and creativity. At a top British high school, one student lists more than ten uses, many of which are comical. Another student, a prodigy with one of the school’s highest IQs, lists just a few uses, all of which are practical. Compared to an IQ test, asking about different uses for a brick might be a better way to identify future Nobel Prize winners.
    Section 5. 
    Terman’s error was using intelligence alone to choose his Termites. While some of the Termites had successful careers, an unexpectedly high went on to careers that even Terman didn’t consider to be successful. The two students tested by Terman’s team who actually did go on to win Nobels were not selected as Termites: their IQs were too low. Terman eventually concluded that “intellect and achievement are far from perfectly correlated.”
    Gladwell states that to understand Chris Langan’s prospects of becoming a “true outlier,” one must learn more about him.
    Analysis: Chapter Three: The Trouble with Geniuses, Part 1 
    Intelligence, Gladwell argues, does not equal success. He dedicates this chapter to the examination of geniuses. Comparing the young subjects of Lewis Terman to Chris Langan, Gladwell argues against Terman’s idea that genius is a key to societal advancement. Gladwell lists Langan’s early accomplishments as a shining example of Terman's idea, then swiftly undercuts expectations. Gladwell argues again that individuals do not succeed or fail solely on their own, but rather due to a constellation of factors, many of which are uncontrollable. Langan's early achievements would suggest great things and a continued path toward accomplishment, but Gladwell includes the anecdote of his game show appearance to undermine the notion that genius equals success. Using two questions from an IQ test, Gladwell introduces the idea of an IQ threshold to examine the the larger notion of intelligence and its limitations. Arguing that the measure of someone’s intelligence is only helpful up to a point, Gladwell uses examples of schools that Nobel laureates attended for undergraduate studies. Some, he points out, are elite institutions; others are not. Additionally, he points to success among graduates of the law school at the University of Michigan. There was no quantifiable difference in success post-graduation between white and POC students, some of whom were admitted under affirmative action with slightly lower undergraduate grades and standardized test scores. Reasonably, then, the level of intelligence beyond a certain point is moot. All of the students were intelligent enough to graduate, and beyond that, he argues, their intelligence predicted nothing.
    Elements other than intelligence must contribute to success. Gladwell expands on his notion of an intelligence threshold and examines these other factors through an example of a question on a divergence test. Using examples of two students at an elite British school, Gladwell shows that the divergence test has no right answers, but instead looks for answers that demonstrate uniqueness and creativity. Intelligence matters, but so does imagination, creativity, and outside-the-box thinking. Gladwell circles back to Terman, reinforcing that the error when choosing his Termites was a focus on intelligence alone. He once again turns his attention to Chris Langan, foreshadowing that Langan’s story did not follow a direct line to achievement. Intelligence alone does not offer a certain path to success.
    Reference
    ',19),o=[n];function r(l,h,c,d,u,m){return a(),t("div",null,o)}const p=e(i,[["render",r]]);export{f as __pageData,p as default};
diff --git a/assets/save_reading_outliers_3.md.20bd5446.lean.js b/assets/save_reading_outliers_3.md.e3dda0fb.lean.js
similarity index 95%
rename from assets/save_reading_outliers_3.md.20bd5446.lean.js
rename to assets/save_reading_outliers_3.md.e3dda0fb.lean.js
index 043f0eb4..437cc5cf 100644
--- a/assets/save_reading_outliers_3.md.20bd5446.lean.js
+++ b/assets/save_reading_outliers_3.md.e3dda0fb.lean.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,d as s}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Three: The Trouble with Geniuses, Part 1","slug":"summary-chapter-three-the-trouble-with-geniuses-part-1","link":"#summary-chapter-three-the-trouble-with-geniuses-part-1","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]}]},{"level":2,"title":"Analysis: Chapter Three: The Trouble with Geniuses, Part 1","slug":"analysis-chapter-three-the-trouble-with-geniuses-part-1","link":"#analysis-chapter-three-the-trouble-with-geniuses-part-1","children":[]}],"relativePath":"save/reading/outliers/3.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/3.md"},n=s("",19),o=[n];function r(l,h,c,d,u,m){return a(),t("div",null,o)}const p=e(i,[["render",r]]);export{f as __pageData,p as default};
+import{_ as e,c as t,o as a,d as s}from"./app.b4df1b52.js";const f=JSON.parse('{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 3: The Trouble with Geniuses, Part 1","description":"Chapter 3 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Three: The Trouble with Geniuses, Part 1","slug":"summary-chapter-three-the-trouble-with-geniuses-part-1","link":"#summary-chapter-three-the-trouble-with-geniuses-part-1","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]}]},{"level":2,"title":"Analysis: Chapter Three: The Trouble with Geniuses, Part 1","slug":"analysis-chapter-three-the-trouble-with-geniuses-part-1","link":"#analysis-chapter-three-the-trouble-with-geniuses-part-1","children":[]}],"relativePath":"save/reading/outliers/3.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/3.md"},n=s("",19),o=[n];function r(l,h,c,d,u,m){return a(),t("div",null,o)}const p=e(i,[["render",r]]);export{f as __pageData,p as default};
diff --git a/assets/save_reading_outliers_4.md.509cd158.js b/assets/save_reading_outliers_4.md.f2e8f102.js
similarity index 99%
rename from assets/save_reading_outliers_4.md.509cd158.js
rename to assets/save_reading_outliers_4.md.f2e8f102.js
index 3528fb75..8767ea23 100644
--- a/assets/save_reading_outliers_4.md.509cd158.js
+++ b/assets/save_reading_outliers_4.md.f2e8f102.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,d as n}from"./app.b4df1b52.js";const g=JSON.parse('{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Four: The Trouble with Geniuses, Part 2","slug":"summary-chapter-four-the-trouble-with-geniuses-part-2","link":"#summary-chapter-four-the-trouble-with-geniuses-part-2","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Four: The Trouble with Geniuses, Part 2","slug":"analysis-chapter-four-the-trouble-with-geniuses-part-2","link":"#analysis-chapter-four-the-trouble-with-geniuses-part-2","children":[]}],"relativePath":"save/reading/outliers/4.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/4.md"},s=n('
    Chapter 4: The Trouble with Geniuses, Part 2 
    Summary: Chapter Four: The Trouble with Geniuses, Part 2 
    Section 1. 
    Chris Langan’s mother had four children, all from different fathers. Her first husband died in Mexico, the second was murdered, the third committed suicide, and the fourth was an abusive alcoholic. Langan says he has never met someone who grew up as impoverished as he and his brothers did. Attending Reed College, in Oregon, on a scholarship, he felt as though he did not belong with the rest of the students. When his mother neglected to fill out the financial aid forms, he lost his scholarship and dropped out. According to Langan, the school just did not care about their students. Later, Langan attended Montana State University in Bozeman but he dropped out when a dean refused Langan’s request to adjust his class schedule because of car trouble. He still has intellectual interests and has been working on a treatise called the “Cognitive Theoretic Model of the Universe.” When asked if, hypothetically, he would take a position at Harvard, he acknowledges the benefit of an environment with so much intellectual energy, but he worries about a lack of intellectual freedom.
    Section 2. 
    Gladwell points out the oddity of Langan’s experiences. Most colleges, especially small ones, try to accommodate student needs. Smart people take positions at places like Harvard instead of in the private sector precisely for the added intellectual freedom. Gladwell contrasts Langan’s story with Robert Oppenheimer’s. While at Cambridge, Oppenheimer became frustrated with his tutor and tried to poison him. After negotiations with the school administration, Oppenheimer was put on probation and assigned to a psychiatrist. Whereas Langan dropped out after his mother failed to fill out paperwork, Oppenheimer managed to stay in college after trying to kill someone. Later, Oppenheimer convinced General Leslie Groves to make Oppenheimer the scientific director of the Manhattan Project. Oppenheimer had the ability to persuade people, where Langan did not.
    Section 3. 
    Psychologist Robert Sternberg calls the ability to persuade someone “practical intelligence.” It involves knowing what to say, how to say it, and when. It requires an ability to read situations. Individuals can have either practical or analytical intelligence, or in the case of Oppenheimer, both. To understand where one obtains practical intelligence, Gladwell refers to a study conducted by Annette Lareau.
    Lareau observed parenting strategies in both Black and white families from different socioeconomic strata. She found two distinct strategies: “concerted cultivation” and “accomplishment of natural growth.” Concerted cultivation, most common in middle-class and wealthier families, is defined by parents’ active promotion of their children’s talents and interests. Accomplishment of natural growth, most common in working-class or impoverished families, is defined by parents’ lack of interest or interaction in their children’s free time. Concerted cultivation, writes Gladwell, encourages children to seek opportunities for growth and to advocate for themselves. Accomplishment of natural growth leaves children unprepared to shape their environment for their own benefit. Concerted cultivation fosters an attitude better suited for success in the modern world.
    Section 4. 
    Oppenheimer was raised by affluent parents who sent him to a progressive private school and took an active interest in his hobbies.
    • Affluent: Having an abundant supply of money or possessions of value.
    By contrast, Chris Langan’s brother Mark states that as children, they learned to resent authority. Mark, too, was unable to obtain financial aid, because he had no knowledge of how the system worked. If Chris Langan had been raised in a family that valued education, he probably would have had more success.
    Section 5. 
    Once the Termites reached working adulthood, Terman grouped 730 of the males into three categories, based on their levels of success. The top 20 percent were upper-class professionals, while the bottom 20 percent had low-paying jobs or were unemployed. After analyzing the differences between the groups, Terman found that the bottom 20 percent came almost entirely from the lowest social and economic classes. What they lacked was “a community around them that prepared them properly for the world.”
    Section 6. 
    Chris Langan lives on a horse farm in Missouri, where he still writes. He is happily married and continues to read physics and philosophy. While he has spent decades on his writing, almost none of it has ever been published. Langan admits he has not tried to contact publishers or found an agent—and does not plan to. Chris Langan did not have the support necessary to meet success. Gladwell points that no one ever makes it alone, regardless of if they are successful musicians, athletes, tech billionaires, or geniuses.
    Analysis: Chapter Four: The Trouble with Geniuses, Part 2 
    Family background plays a crucial role in an individual’s success. While a genius like Chris Langan should thrive on a college campus, he drops out. Langan doesn’t struggle with academics, but with paperwork, procedures, and environment. Gladwell’s characterization of Langan almost makes him seem like two separate characters: a confident, genius game show contestant versus a child from a poor and troubled family. Langan may be a true outlier in the sense that he doesn’t seem to fit in academia or the working-class world.  Langan’s story is ironic. His brilliant mind should propel him to success. However, his story also perfectly proves Gladwell’s point that brainpower alone does not lead to success. The author delves deeper into the irony of Langan’s situation by comparing him to Robert Oppenheimer, who worked on the nuclear bomb during World War II. Like Langan, Oppenheimer possesses great intelligence. Unlike Langan, Oppenheimer has an understanding that allows him to navigate the world effectively. Oppenheimer knows how to combat challenges, where Langan gets bested by a financial aid problem and class schedule. Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority. Without a family background that encourages success, intelligence is not enough.
    Contrast & Comparison
    Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority.
    The power of persuasion is an important factor that drives success. Gladwell notes that the power of persuasion is practical intelligence. He contrasts practical intelligence with analytical ability, noting that just because a person is smart does not mean they have practical intelligence. These two types of knowledge are not necessarily coeval. He reinforces this point with a return to the comparison of Langan and Oppenheimer. Both men are exceedingly intelligent, but Langan lacks the social savvy of practical intelligence. Gladwell suggests that individuals gain practical intelligence skills from their families, discussing a study by sociologist Annette Lareau to prove his point. Children from wealthier families learn how to interact with society in a way that drives achievement. Successful people have the power of persuasion and can convince others to see things from their point of view.
    Success, then, depends on more than individual effort. Gladwell builds this argument by detailing the differences between Oppenheimer’s upbringing and Langan’s. Oppenheimer lived in an upper-class neighborhood with myriad advantages. He learned how to negotiate and stand up for himself. Langan’s family moved from place to place, struggling for jobs, money, food, and clothes, and Langan learned that he couldn’t rely on others. Gladwell's consideration of the Termites' success or struggles as adults supports his assertion that success is more than an individual effort; Gladwell states, “In the end, only one thing mattered: family background.” Terman’s findings and Gladwell’s conclusion do not mean that talented individuals from lower social and economic classes cannot have successful futures. To succeed, everyone needs help along the way, if not from family, then from a supportive community. Individuals do not achieve success solely on their own.
    Reference
    ',23),o=[s];function r(l,h,c,d,u,p){return a(),t("div",null,o)}const f=e(i,[["render",r]]);export{g as __pageData,f as default};
+import{_ as e,c as t,o as a,d as n}from"./app.b4df1b52.js";const g=JSON.parse('{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Four: The Trouble with Geniuses, Part 2","slug":"summary-chapter-four-the-trouble-with-geniuses-part-2","link":"#summary-chapter-four-the-trouble-with-geniuses-part-2","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Four: The Trouble with Geniuses, Part 2","slug":"analysis-chapter-four-the-trouble-with-geniuses-part-2","link":"#analysis-chapter-four-the-trouble-with-geniuses-part-2","children":[]}],"relativePath":"save/reading/outliers/4.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/4.md"},s=n('
    Chapter 4: The Trouble with Geniuses, Part 2 
    Summary: Chapter Four: The Trouble with Geniuses, Part 2 
    Section 1. 
    Chris Langan’s mother had four children, all from different fathers. Her first husband died in Mexico, the second was murdered, the third committed suicide, and the fourth was an abusive alcoholic. Langan says he has never met someone who grew up as impoverished as he and his brothers did. Attending Reed College, in Oregon, on a scholarship, he felt as though he did not belong with the rest of the students. When his mother neglected to fill out the financial aid forms, he lost his scholarship and dropped out. According to Langan, the school just did not care about their students. Later, Langan attended Montana State University in Bozeman but he dropped out when a dean refused Langan’s request to adjust his class schedule because of car trouble. He still has intellectual interests and has been working on a treatise called the “Cognitive Theoretic Model of the Universe.” When asked if, hypothetically, he would take a position at Harvard, he acknowledges the benefit of an environment with so much intellectual energy, but he worries about a lack of intellectual freedom.
    Section 2. 
    Gladwell points out the oddity of Langan’s experiences. Most colleges, especially small ones, try to accommodate student needs. Smart people take positions at places like Harvard instead of in the private sector precisely for the added intellectual freedom. Gladwell contrasts Langan’s story with Robert Oppenheimer’s. While at Cambridge, Oppenheimer became frustrated with his tutor and tried to poison him. After negotiations with the school administration, Oppenheimer was put on probation and assigned to a psychiatrist. Whereas Langan dropped out after his mother failed to fill out paperwork, Oppenheimer managed to stay in college after trying to kill someone. Later, Oppenheimer convinced General Leslie Groves to make Oppenheimer the scientific director of the Manhattan Project. Oppenheimer had the ability to persuade people, where Langan did not.
    Section 3. 
    Psychologist Robert Sternberg calls the ability to persuade someone “practical intelligence.” It involves knowing what to say, how to say it, and when. It requires an ability to read situations. Individuals can have either practical or analytical intelligence, or in the case of Oppenheimer, both. To understand where one obtains practical intelligence, Gladwell refers to a study conducted by Annette Lareau.
    Lareau observed parenting strategies in both Black and white families from different socioeconomic strata. She found two distinct strategies: “concerted cultivation” and “accomplishment of natural growth.” Concerted cultivation, most common in middle-class and wealthier families, is defined by parents’ active promotion of their children’s talents and interests. Accomplishment of natural growth, most common in working-class or impoverished families, is defined by parents’ lack of interest or interaction in their children’s free time. Concerted cultivation, writes Gladwell, encourages children to seek opportunities for growth and to advocate for themselves. Accomplishment of natural growth leaves children unprepared to shape their environment for their own benefit. Concerted cultivation fosters an attitude better suited for success in the modern world.
    Section 4. 
    Oppenheimer was raised by affluent parents who sent him to a progressive private school and took an active interest in his hobbies.
    • Affluent: Having an abundant supply of money or possessions of value.
    By contrast, Chris Langan’s brother Mark states that as children, they learned to resent authority. Mark, too, was unable to obtain financial aid, because he had no knowledge of how the system worked. If Chris Langan had been raised in a family that valued education, he probably would have had more success.
    Section 5. 
    Once the Termites reached working adulthood, Terman grouped 730 of the males into three categories, based on their levels of success. The top 20 percent were upper-class professionals, while the bottom 20 percent had low-paying jobs or were unemployed. After analyzing the differences between the groups, Terman found that the bottom 20 percent came almost entirely from the lowest social and economic classes. What they lacked was “a community around them that prepared them properly for the world.”
    Section 6. 
    Chris Langan lives on a horse farm in Missouri, where he still writes. He is happily married and continues to read physics and philosophy. While he has spent decades on his writing, almost none of it has ever been published. Langan admits he has not tried to contact publishers or found an agent—and does not plan to. Chris Langan did not have the support necessary to meet success. Gladwell points that no one ever makes it alone, regardless of if they are successful musicians, athletes, tech billionaires, or geniuses.
    Analysis: Chapter Four: The Trouble with Geniuses, Part 2 
    Family background plays a crucial role in an individual’s success. While a genius like Chris Langan should thrive on a college campus, he drops out. Langan doesn’t struggle with academics, but with paperwork, procedures, and environment. Gladwell’s characterization of Langan almost makes him seem like two separate characters: a confident, genius game show contestant versus a child from a poor and troubled family. Langan may be a true outlier in the sense that he doesn’t seem to fit in academia or the working-class world.  Langan’s story is ironic. His brilliant mind should propel him to success. However, his story also perfectly proves Gladwell’s point that brainpower alone does not lead to success. The author delves deeper into the irony of Langan’s situation by comparing him to Robert Oppenheimer, who worked on the nuclear bomb during World War II. Like Langan, Oppenheimer possesses great intelligence. Unlike Langan, Oppenheimer has an understanding that allows him to navigate the world effectively. Oppenheimer knows how to combat challenges, where Langan gets bested by a financial aid problem and class schedule. Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority. Without a family background that encourages success, intelligence is not enough.
    Contrast & Comparison
    Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority.
    The power of persuasion is an important factor that drives success. Gladwell notes that the power of persuasion is practical intelligence. He contrasts practical intelligence with analytical ability, noting that just because a person is smart does not mean they have practical intelligence. These two types of knowledge are not necessarily coeval. He reinforces this point with a return to the comparison of Langan and Oppenheimer. Both men are exceedingly intelligent, but Langan lacks the social savvy of practical intelligence. Gladwell suggests that individuals gain practical intelligence skills from their families, discussing a study by sociologist Annette Lareau to prove his point. Children from wealthier families learn how to interact with society in a way that drives achievement. Successful people have the power of persuasion and can convince others to see things from their point of view.
    Success, then, depends on more than individual effort. Gladwell builds this argument by detailing the differences between Oppenheimer’s upbringing and Langan’s. Oppenheimer lived in an upper-class neighborhood with myriad advantages. He learned how to negotiate and stand up for himself. Langan’s family moved from place to place, struggling for jobs, money, food, and clothes, and Langan learned that he couldn’t rely on others. Gladwell's consideration of the Termites' success or struggles as adults supports his assertion that success is more than an individual effort; Gladwell states, “In the end, only one thing mattered: family background.” Terman’s findings and Gladwell’s conclusion do not mean that talented individuals from lower social and economic classes cannot have successful futures. To succeed, everyone needs help along the way, if not from family, then from a supportive community. Individuals do not achieve success solely on their own.
    Reference
    ',23),o=[s];function r(l,h,c,d,u,p){return a(),t("div",null,o)}const f=e(i,[["render",r]]);export{g as __pageData,f as default};
diff --git a/assets/save_reading_outliers_4.md.509cd158.lean.js b/assets/save_reading_outliers_4.md.f2e8f102.lean.js
similarity index 95%
rename from assets/save_reading_outliers_4.md.509cd158.lean.js
rename to assets/save_reading_outliers_4.md.f2e8f102.lean.js
index 30b056e2..ab14c2fe 100644
--- a/assets/save_reading_outliers_4.md.509cd158.lean.js
+++ b/assets/save_reading_outliers_4.md.f2e8f102.lean.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,d as n}from"./app.b4df1b52.js";const g=JSON.parse('{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Four: The Trouble with Geniuses, Part 2","slug":"summary-chapter-four-the-trouble-with-geniuses-part-2","link":"#summary-chapter-four-the-trouble-with-geniuses-part-2","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Four: The Trouble with Geniuses, Part 2","slug":"analysis-chapter-four-the-trouble-with-geniuses-part-2","link":"#analysis-chapter-four-the-trouble-with-geniuses-part-2","children":[]}],"relativePath":"save/reading/outliers/4.md","lastUpdated":1679649941000}'),i={name:"save/reading/outliers/4.md"},s=n("",23),o=[s];function r(l,h,c,d,u,p){return a(),t("div",null,o)}const f=e(i,[["render",r]]);export{g as __pageData,f as default};
+import{_ as e,c as t,o as a,d as n}from"./app.b4df1b52.js";const g=JSON.parse('{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes","frontmatter":{"title":"Chapter 4: The Trouble with Geniuses, Part 2","description":"Chapter 4 summary of novel Outliers from Sparknotes"},"headers":[{"level":2,"title":"Summary: Chapter Four: The Trouble with Geniuses, Part 2","slug":"summary-chapter-four-the-trouble-with-geniuses-part-2","link":"#summary-chapter-four-the-trouble-with-geniuses-part-2","children":[{"level":3,"title":"Section 1.","slug":"section-1","link":"#section-1","children":[]},{"level":3,"title":"Section 2.","slug":"section-2","link":"#section-2","children":[]},{"level":3,"title":"Section 3.","slug":"section-3","link":"#section-3","children":[]},{"level":3,"title":"Section 4.","slug":"section-4","link":"#section-4","children":[]},{"level":3,"title":"Section 5.","slug":"section-5","link":"#section-5","children":[]},{"level":3,"title":"Section 6.","slug":"section-6","link":"#section-6","children":[]}]},{"level":2,"title":"Analysis: Chapter Four: The Trouble with Geniuses, Part 2","slug":"analysis-chapter-four-the-trouble-with-geniuses-part-2","link":"#analysis-chapter-four-the-trouble-with-geniuses-part-2","children":[]}],"relativePath":"save/reading/outliers/4.md","lastUpdated":1679745767000}'),i={name:"save/reading/outliers/4.md"},s=n("",23),o=[s];function r(l,h,c,d,u,p){return a(),t("div",null,o)}const f=e(i,[["render",r]]);export{g as __pageData,f as default};
diff --git a/feed.rss b/feed.rss
new file mode 100644
index 00000000..a46709a2
--- /dev/null
+++ b/feed.rss
@@ -0,0 +1,64 @@
+
+
+    
+        VitePress
+        https://note.toshiki.dev
+        A VitePress site
+        Sat, 25 Mar 2023 12:04:00 GMT
+        https://validator.w3.org/feed/docs/rss2.html
+        https://github.com/jpmonette/feed
+        en-US
+        
+            VitePress
+            https://note.toshiki.dev/logos/logo-308px.png
+            https://note.toshiki.dev
+        
+        -
+        
+            https://note.toshiki.devroadmap.html
+            https://note.toshiki.devroadmap.html
+            
    Toshiki's Note
    Appearance
    TOC
    Theme 
    Homepage 
    •  Finish three hero action blocks with keywords and its corresponded descriptions.
    •  Finish my learning platform section using SVGs of different online academies from simple icons.
      • Descriptions
      • Icon in SVG format
      • Platform name
      • Linkable SVG icon/button
        •  Khan academy
        •  GitHub
        •  Libretext
        •  OpenStax
        •  BCcampus
        •  Wikibooks
        •  Wikipedia
        •  Bookboon
        • [ ]
    Configs 
    •  Header configs including different properties and meta configs.
    •  Complete navigation configuration. 
    •  Complete sidebar configs for different directories.
    •  Vitepress sidebar generation plugin for huge bundled clips article directory.
    Articles 
    •  <head> tag documentation or guide by joshbuchea/HEAD.
    •  Write index page for every directory, no Chat GPT allowed.
    •  Chemistry review notes.
    •  JavaScript 0-100 notes per chapter. 
      • Marijn Haverbeke - Eloquent JavaScript_ A Modern Introduction to Programming (2011, No Starch Press)
    •  Outliers novel clips
    •  Migrate clipped articles and archives from Notion to Vitepress.
    •  Fresh copy of "How To Ask Questions The Smart Way" by Eric Steven Raymond 
    
+    
+    
+    
+  ]]>
+        
+        
+            <![CDATA[Toshiki's Notebook]]>
+            https://note.toshiki.devindex.html
+            https://note.toshiki.devindex.html
+            
    Toshiki's Note
    Appearance
    Toshiki's Notebook
    Research & Produce
    👨‍💻 Eternal & digital knowledge base for content craetion and notes management.
    👉 Start Reading
    🗒️ View on GitHub
    Home logo
    🕒
    Tempus Fugit
    Tempus Fugit, which means "time flies" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential.
    ☕
    Carpe Diem
    Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning.
    💡
    Epiphania
    An epiphany, derived from the Latin word "epiphania," is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas.

+    
+    
+    
+  ]]>
+        
+        
+            <![CDATA[Git push results in "Authentication Failed”]]>
+            https://note.toshiki.devgetting-started.html
+            https://note.toshiki.devgetting-started.html
+            
Toshiki's Note
Appearance
TOC
Git push results in "Authentication Failed” 
Issue 
bash
$ git push
+Username for 'https://github.com': ${{ GITHUB_USERNAME }}
+Password for 'https://andatoshiki@github.com': ${{ GITHUB_PASSWORD }} # or GitHub personal access token
+remote: Invalid username or password.
+fatal: Authentication failed for 'https://github.com/andatoshiki/andatoshiki.git/'
+
$ git push
+Username for 'https://github.com': ${{ GITHUB_USERNAME }}
+Password for 'https://andatoshiki@github.com': ${{ GITHUB_PASSWORD }} # or GitHub personal access token
+remote: Invalid username or password.
+fatal: Authentication failed for 'https://github.com/andatoshiki/andatoshiki.git/'
+
git push to GitHub remote branch failed via https protocol
Solution 
Solution 1 
If you enabled two-factor authentication in your GitHub account you won't be able to push via HTTPS using your accounts password. Instead you need to generate a personal access token. This can be done in the application settings of your GitHub account. Using this token as your password should allow you to push to your remote repository via HTTPS. Use your username as usual.
You may also need to update the origin for your repository if it is set to HTTPS. Do this to switch to SSH:
bash
$ git remote -v
+$ git remote set-url origin git@github.com:$USERNAME/$REPONAME.git
+
$ git remote -v
+$ git remote set-url origin git@github.com:$USERNAME/$REPONAME.git
+
Solution 2 
GitHub username & password/access token mismatched due to prior temporary Git config setup → Reset Git global username & email config or in current repository
To set your global username/email configuration:
  1. Open the command line.
  2. Set your username: git config --global user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config --global user.email "MY_NAME@example.com"
To set repository-specific username/email configuration:
  1. From the command line, change into the repository directory.
  2. Set your username: git config user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config user.email "MY_NAME@example.com"
  4. Verify your configuration by displaying your configuration file: cat .git/config

+    
+    
+    
+  ]]>
+        
+    
+
\ No newline at end of file
diff --git a/getting-started.html b/getting-started.html
index d125de1f..8cecf7e9 100644
--- a/getting-started.html
+++ b/getting-started.html
@@ -8,7 +8,7 @@
     
     
     
-    
+    
     
     
   
@@ -44,8 +44,8 @@
 $ git remote set-url origin git@github.com:$USERNAME/$REPONAME.git
 
$ git remote -v
 $ git remote set-url origin git@github.com:$USERNAME/$REPONAME.git
-
Solution 2 
GitHub username & password/access token mismatched due to prior temporary Git config setup → Reset Git global username & email config or in current repository
To set your global username/email configuration:
  1. Open the command line.
  2. Set your username: git config --global user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config --global user.email "MY_NAME@example.com"
To set repository-specific username/email configuration:
  1. From the command line, change into the repository directory.
  2. Set your username: git config user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config user.email "MY_NAME@example.com"
  4. Verify your configuration by displaying your configuration file: cat .git/config
- +

Solution 2

GitHub username & password/access token mismatched due to prior temporary Git config setup → Reset Git global username & email config or in current repository

To set your global username/email configuration:

  1. Open the command line.
  2. Set your username: git config --global user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config --global user.email "MY_NAME@example.com"

To set repository-specific username/email configuration:

  1. From the command line, change into the repository directory.
  2. Set your username: git config user.name "FIRST_NAME LAST_NAME"
  3. Set your email address: git config user.email "MY_NAME@example.com"
  4. Verify your configuration by displaying your configuration file: cat .git/config
+ diff --git a/hashmap.json b/hashmap.json index e4223238..20547284 100644 --- a/hashmap.json +++ b/hashmap.json @@ -1 +1 @@ -{"academic_chemistry_index.md":"fa53861e","academic_chemistry_problems_03-02-2.md":"9190de7a","academic_physics_ipho-formulas-jpn_3.md":"ebe05286","academic_literature_writing_methods-of-development.md":"789cc26c","academic_chemistry_problems_02-20.md":"34de7858","academic_chemistry_problems_03-02-3.md":"c0d95fdc","academic_chemistry_problems_03-02-1.md":"9ed41a38","academic_physics_ipho-formulas-jpn_12.md":"b36f34f2","academic_physics_ipho-formulas-jpn_2.md":"5f49d39f","academic_physics_ipho-formulas-jpn_4.md":"eeb6afee","academic_vocabulary_2023_02_2023-02-27.md":"67fda3b7","academic_vocabulary_index.md":"bd7d9e30","academic_literature_index.md":"cf2b2a11","academic_physics_ipho-formulas-jpn_5.md":"8fecd163","academic_physics_ipho-formulas-jpn_6.md":"0fa33499","academic_physics_ipho-formulas-jpn_7.md":"4d700c2a","academic_physics_ipho-formulas-jpn_9.md":"4790c4ee","application_markdown-it-katex_how-to-use.md":"86b38519","getting-started.md":"e767a449","index.md":"cb83f397","javascript_notes_1_1-1.md":"82d73735","javascript_notes_1_1-2.md":"6a7421a9","roadmap.md":"958d3e89","save_reading_index.md":"3a052c6c","save_reading_outliers_1.md":"bc528405","save_reading_outliers_2.md":"93d4b0ec","save_reading_outliers_3.md":"20bd5446","save_reading_outliers_4.md":"509cd158","academic_physics_ipho-formulas-jpn_11.md":"b8b41f81","academic_chemistry_notes_12-5.md":"c1e408a4","academic_physics_ipho-formulas-jpn_8.md":"6b85a478","academic_physics_ipho-formulas-jpn_1.md":"00b662f0","academic_physics_index.md":"735544d4","academic_physics_ipho-formulas-jpn_10.md":"75467e68","academic_physics_ipho-formulas-jpn_13.md":"ffe70365","application_markdown-it-katex_support-function.md":"80d3ff38","application_markdown-it-katex_support-table.md":"43ca6e38"} +{"academic_physics_ipho-formulas-jpn_10.md":"be9b3422","academic_physics_ipho-formulas-jpn_8.md":"0f5a7d43","academic_physics_ipho-formulas-jpn_11.md":"822ff406","academic_physics_ipho-formulas-jpn_12.md":"a7d0b69c","academic_physics_ipho-formulas-jpn_1.md":"7dca7f3d","academic_physics_ipho-formulas-jpn_13.md":"316c8041","academic_physics_ipho-formulas-jpn_3.md":"7ff0d522","academic_physics_ipho-formulas-jpn_4.md":"9d0702e3","academic_physics_ipho-formulas-jpn_7.md":"23ff3e50","academic_physics_ipho-formulas-jpn_6.md":"2c0492de","academic_chemistry_index.md":"7e5c2af2","academic_physics_ipho-formulas-jpn_5.md":"6e825113","academic_chemistry_problems_03-02-1.md":"81d46b6c","academic_chemistry_problems_02-20.md":"3b68d95a","academic_chemistry_problems_03-02-2.md":"ae6c679d","academic_chemistry_problems_03-02-3.md":"19495002","academic_physics_index.md":"e4b9ed9a","academic_chemistry_notes_12-5.md":"c2054313","academic_literature_index.md":"04e7fa0a","academic_literature_writing_methods-of-development.md":"8e5018c2","academic_vocabulary_2023_02_2023-02-27.md":"7854c559","academic_vocabulary_index.md":"7862edfa","getting-started.md":"8714bbcf","javascript_notes_1_1-2.md":"237686b4","roadmap.md":"c1d06e8e","save_reading_index.md":"b8540279","save_reading_outliers_1.md":"457f7212","save_reading_outliers_2.md":"57cc24bd","save_reading_outliers_3.md":"e3dda0fb","save_reading_outliers_4.md":"f2e8f102","academic_physics_ipho-formulas-jpn_2.md":"d06c6e69","index.md":"c6aabed9","javascript_notes_1_1-1.md":"1269f243","academic_physics_ipho-formulas-jpn_9.md":"5873a4aa","application_markdown-it-katex_how-to-use.md":"93aa4553","application_markdown-it-katex_support-function.md":"8824ed46","application_markdown-it-katex_support-table.md":"56929713"} diff --git a/index.html b/index.html index 0b62be67..f7e75045 100644 --- a/index.html +++ b/index.html @@ -8,7 +8,7 @@ - + @@ -31,7 +31,7 @@
Toshiki's Note

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Tempus Fugit

Tempus Fugit, which means "time flies" in Latin, is a phrase that highlights the fact that every person has the same 24 hours per day to learn. However, this time is never enough to learn everything. That's why recording knowledge for review is essential.

☕

Carpe Diem

Carpe Diem, take it slow, seize the day and savor its moments. Enjoy a cup of coffee while playing blues on a 1980s-style CD player. Turn off the lights, close the curtains, and let the small lamp illuminate the space. The time is yours, relish the day, and unleash the productivity while learning.

💡

Epiphania

An epiphany, derived from the Latin word "epiphania," is a moment of sudden and brilliant realization or insight. These moments of clarity and inspiration are precious and should be treated as such; to ensure that we don't forget these valuable ideas.

- + diff --git a/javascript/notes/1/1-1.html b/javascript/notes/1/1-1.html index 51d1e9cd..fa6a5893 100644 --- a/javascript/notes/1/1-1.html +++ b/javascript/notes/1/1-1.html @@ -8,7 +8,7 @@ - + @@ -66,8 +66,8 @@ 
A newline character is written like "\n".

the backslash character (\) is used as an escape character to indicate that the following character(s) should be treated specially. In this case, the "\n" sequence is an escape sequence that represents a newline character. The backslash before the n character tells the JavaScript interpreter that it should treat the n as a special character and not just as the letter "n".

However, if we want to include an actual backslash character (\), we will have to escape it by using to two backslashes \\, or else with one single slash the JavaScript interpreter will still determines it as an special operator, Thus \\ will print \ on output.

  • But what about the quotation marks used within the quotation marks that wraps the string? Wouldn't JavaScript interpreter throw error?

    • In the given JavaScript string, the inner set of double quotation marks ("\\n") is escaped using a backslash (\) character. This tells the JavaScript interpreter to treat the inner double quotation marks as a regular character instead of a string delimiter.

      So when the string is rendered on output, the backslash character will be removed and the inner set of quotation marks will be displayed as a regular character. The rendered string will look like this,

      js
      '\n'
 
      '\n'
-

      The outer set of double quotation marks in the original string delimit the entire string and will be displayed as regular quotation marks.

Source: ChatGPT CA (Code Analysis)

- +

The outer set of double quotation marks in the original string delimit the entire string and will be displayed as regular quotation marks.

Source: ChatGPT CA (Code Analysis)

+ diff --git a/javascript/notes/1/1-2.html b/javascript/notes/1/1-2.html index 578a0121..14e1b13c 100644 --- a/javascript/notes/1/1-2.html +++ b/javascript/notes/1/1-2.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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+ diff --git a/roadmap.html b/roadmap.html index e6350123..1cd1ef3e 100644 --- a/roadmap.html +++ b/roadmap.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Theme

Homepage

  • Finish three hero action blocks with keywords and its corresponded descriptions.

  • Finish my learning platform section using SVGs of different online academies from simple icons.

    • Descriptions

    • Icon in SVG format

    • Platform name

    • Linkable SVG icon/button

      • Khan academy
      • GitHub
      • Libretext
      • OpenStax
      • BCcampus
      • Wikibooks
      • Wikipedia
      • Bookboon
      • [ ]

Configs

  • Header configs including different properties and meta configs.
  • Complete navigation configuration.
  • Complete sidebar configs for different directories.
  • Vitepress sidebar generation plugin for huge bundled clips article directory.

Articles

  • <head> tag documentation or guide by joshbuchea/HEAD.
  • Write index page for every directory, no Chat GPT allowed.
  • Chemistry review notes.
  • JavaScript 0-100 notes per chapter.
    • Marijn Haverbeke - Eloquent JavaScript_ A Modern Introduction to Programming (2011, No Starch Press)
  • Outliers novel clips
  • Migrate clipped articles and archives from Notion to Vitepress.
  • Fresh copy of "How To Ask Questions The Smart Way" by Eric Steven Raymond
- +
Toshiki's Note

Appearance

TOC

Theme

Homepage

  • Finish three hero action blocks with keywords and its corresponded descriptions.

  • Finish my learning platform section using SVGs of different online academies from simple icons.

    • Descriptions

    • Icon in SVG format

    • Platform name

    • Linkable SVG icon/button

      • Khan academy
      • GitHub
      • Libretext
      • OpenStax
      • BCcampus
      • Wikibooks
      • Wikipedia
      • Bookboon
      • [ ]

Configs

  • Header configs including different properties and meta configs.
  • Complete navigation configuration.
  • Complete sidebar configs for different directories.
  • Vitepress sidebar generation plugin for huge bundled clips article directory.

Articles

  • <head> tag documentation or guide by joshbuchea/HEAD.
  • Write index page for every directory, no Chat GPT allowed.
  • Chemistry review notes.
  • JavaScript 0-100 notes per chapter.
    • Marijn Haverbeke - Eloquent JavaScript_ A Modern Introduction to Programming (2011, No Starch Press)
  • Outliers novel clips
  • Migrate clipped articles and archives from Notion to Vitepress.
  • Fresh copy of "How To Ask Questions The Smart Way" by Eric Steven Raymond
+ diff --git a/save/reading/index.html b/save/reading/index.html index 4ad3b678..4270758d 100644 --- a/save/reading/index.html +++ b/save/reading/index.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ - - + + diff --git a/save/reading/outliers/1.html b/save/reading/outliers/1.html index 380d82bc..aa9fd055 100644 --- a/save/reading/outliers/1.html +++ b/save/reading/outliers/1.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Introduction & Chapter 1: The Roseto Mystery

Summary: Introduction: The Roseto Mystery

Section 1.

In the late 1800s, immigrants from Roseto Valfortore, Italy, came to Pennsylvania to work in the slate quarry near the town of Bangor. The settlers established a new community, named after their old one: Roseto. They built schools, a park, small shops, and more than a dozen factories. They kept to themselves and did not interact much with the predominantly German and English populations of the towns around them.

In the 1950s, a local doctor told Stewart Wolf, a medical researcher, that hardly anyone in Roseto under age sixty-five had heart disease. Wolf was curious. He did blood draws and EKG scans, and he analyzed physicians’ records and death certificates. Wolf was amazed that almost no one under fifty-five showed any signs of heart disease, which at the time was America’s leading cause of death in men under sixty-five. Wolf enlisted the help of John Bruhn, a sociologist. They found that there was no suicide, alcoholism, or drug addiction in Roseto: everyone seemed to be dying of old age. According to Gladwell, Roseto was an outlier.

Section 2.

Wolf was forced to rule out diet and lifestyle as explanations, because the Rosetans had poor eating habits, smoked heavily, and were obese. He ruled out genetics after determining that Rosetans’ relatives in other parts of the country were not in comparably good health. Wolf eventually decided that what made Roseto’s inhabitants so healthy was the town itself—its culture and social structure. Many homes contained three generations living together, and with a population of just two thousand people, there were twenty-two separate civic organizations.

Wolf and Bruhn were met with a great deal of skepticism. They had to work hard to convince the medical establishment that the values of where we live and the people around us have a significant impact on who we are. Gladwell wants Outliers to do for our understanding of success what Wolf did for our understanding of health.

Summary: Chapter One: The Matthew Effect

Section 1.

Gladwell describes a game between two teams in the Canadian Hockey League, the most competitive junior hockey league in the world. Starting at a very young age, players are regularly assessed for talent, so that the best can be separated out and prepared for the next level. The system is designed to be a meritocracy.

Section 2.

Gladwell wants to show that circumstances matter just as much for success as work ethic or intelligence. People often ask about the lifestyle, intelligence, or special talents of successful individuals, but not enough people ask when and where a person grew up. Gladwell likens people to trees: we all know that the tallest trees received the most sunlight, had nutrient-rich soil, and were lucky enough to avoid lumberjacks. He suggests that we study the environmental and social influences that make people successful.

Section 3.

In the 1980s, Canadian psychologist Roger Barnsley observed that on elite Canadian hockey teams, whether youth league or NHL, a disproportionate number of players have birthdays in the first three months of the year.

Section 4.

The explanation for the distribution of birthdays is simple: the cutoff date for an individual’s league assignment is January 1. A player born on January 2 will be 12 months older than one born at the end of December. At the age of nine or ten, this often translates into a huge difference in size, coordination, and maturity. By age ten, coaches regularly pick the oldest and largest potential players for the more competitive “rep squads,” where the players will receive better coaching, have more practice time, and play many more games. By thirteen or fourteen, all of the extra experience and coaching will have actually made the players better, and they will be selected for the more competitive league(s). The same thing happens in American youth baseball and European soccer, but with different cutoff dates.

The phenomenon is also observable in education. Economists Kelly Bedard and Elizabeth Dhuey found that on math and science tests, the older children in fourth grade regularly score better than the youngest children. This can affect whether a child qualifies for a gifted program. When Bedard and Dhuey extended their analysis to four-year colleges, they found that the students who belonged to the relatively youngest group were underrepresented by more than 10 percent.

Section 5.

The top-level hockey players were given opportunities they neither deserved nor earned. Sociologist Robert Merton called this the “Matthew Effect,” after the verse in the Gospel of Matthew:

“For unto everyone that hath shall be given, and he shall have abundance. But from that hath not shall be taken away even that which he hath.”

The successful receive more resources: the best students receive the best teaching, the richest citizens get the biggest tax breaks, the largest kids get the best coaching. Sociologists call this “accumulative advantage.” Gladwell points out that cutoff dates exclude nearly half of the potential athletes from a population. Junior hockey teams in the Czech Republic show the same unbalanced distribution of birthdays as in Canada. If Canada or the Czech Republic separated each of their youth leagues into two separate leagues, one for kids born in the first half of the year, and one for kids born in the second half of the year, they would have twice as many athletes available for their national teams. Similarly, schools could separate kindergarten classes into students born in the first, middle, and last four months of the year. The benefits would justify the added administrative work, but, writes Gladwell, the scheme would run afoul of society’s need to believe that individual merit matters more than the rules society has created.

Section 6.

Gord Wasden, the father of one of the Canadian Hockey League boys from the first section, describes his son. Scott Wasden worked hard to get where he is, but he has also generally had the advantage of being big compared to others on his team. He was born on January 4.

Analysis: Introduction: The Roseto Mystery & Chapter 1: The Matthew Effect

Gladwell's thesis argues that that the idea of rugged, individual success is not accurate. Rather, the most successful person doesn’t thrive without some environmental and social influence plus a dose of good fortune.  After laying out the concepts of a meritocracy and suggesting that this is the way that hockey players advance in Canada, he immediately undercuts this idea. Gladwell uses the illustration of birthday distribution as an example of an invisible contributor to the success of hockey players. With a registration cutoff date of January 1, players born from January 2 through March 31 are older than teammates born later in the year. These older players are likely bigger, faster, more coordinated, and more mature. Since the older players are seen as more skilled, they get selected for more advanced leagues with more practice, more games, and higher-quality coaching. By the time these older players reach their early teens, the extra advantages gained from being judged better because of their birthday translate into being better players. Similarly, the age cutoff for school registrations often mistakes maturity for ability. As a result, the older children appear smarter, get put into advanced groups, and qualify for gifted programs. The birthdate bias carries through to college.

Advantages result in more advantages. Gladwell reinforces this idea with the “Matthew Effect,” which states that "success leads to more success." More simply: by being a little bit better, a hockey player will get opportunities that may result in the player becoming an outlier. Gladwell implies that the systems that determine success are not efficient. He asks readers to question the way we, as a society, think about success. He suggests that changing the systems in athletics and education would chip away at the myth of individual merit as the chief marker of success and help level the playing field. Gladwell's model for this phenomenon is hockey player Scott Wasden. By demonstrating that Scott had the passion, talent, and work ethic for the game, as well as the good luck to be born on January 4, Gladwell reasons that Wasden, like many others he will be profiling, benefit by being both good and lucky.

Reference

- +
Toshiki's Note

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TOC

Introduction & Chapter 1: The Roseto Mystery

Summary: Introduction: The Roseto Mystery

Section 1.

In the late 1800s, immigrants from Roseto Valfortore, Italy, came to Pennsylvania to work in the slate quarry near the town of Bangor. The settlers established a new community, named after their old one: Roseto. They built schools, a park, small shops, and more than a dozen factories. They kept to themselves and did not interact much with the predominantly German and English populations of the towns around them.

In the 1950s, a local doctor told Stewart Wolf, a medical researcher, that hardly anyone in Roseto under age sixty-five had heart disease. Wolf was curious. He did blood draws and EKG scans, and he analyzed physicians’ records and death certificates. Wolf was amazed that almost no one under fifty-five showed any signs of heart disease, which at the time was America’s leading cause of death in men under sixty-five. Wolf enlisted the help of John Bruhn, a sociologist. They found that there was no suicide, alcoholism, or drug addiction in Roseto: everyone seemed to be dying of old age. According to Gladwell, Roseto was an outlier.

Section 2.

Wolf was forced to rule out diet and lifestyle as explanations, because the Rosetans had poor eating habits, smoked heavily, and were obese. He ruled out genetics after determining that Rosetans’ relatives in other parts of the country were not in comparably good health. Wolf eventually decided that what made Roseto’s inhabitants so healthy was the town itself—its culture and social structure. Many homes contained three generations living together, and with a population of just two thousand people, there were twenty-two separate civic organizations.

Wolf and Bruhn were met with a great deal of skepticism. They had to work hard to convince the medical establishment that the values of where we live and the people around us have a significant impact on who we are. Gladwell wants Outliers to do for our understanding of success what Wolf did for our understanding of health.

Summary: Chapter One: The Matthew Effect

Section 1.

Gladwell describes a game between two teams in the Canadian Hockey League, the most competitive junior hockey league in the world. Starting at a very young age, players are regularly assessed for talent, so that the best can be separated out and prepared for the next level. The system is designed to be a meritocracy.

Section 2.

Gladwell wants to show that circumstances matter just as much for success as work ethic or intelligence. People often ask about the lifestyle, intelligence, or special talents of successful individuals, but not enough people ask when and where a person grew up. Gladwell likens people to trees: we all know that the tallest trees received the most sunlight, had nutrient-rich soil, and were lucky enough to avoid lumberjacks. He suggests that we study the environmental and social influences that make people successful.

Section 3.

In the 1980s, Canadian psychologist Roger Barnsley observed that on elite Canadian hockey teams, whether youth league or NHL, a disproportionate number of players have birthdays in the first three months of the year.

Section 4.

The explanation for the distribution of birthdays is simple: the cutoff date for an individual’s league assignment is January 1. A player born on January 2 will be 12 months older than one born at the end of December. At the age of nine or ten, this often translates into a huge difference in size, coordination, and maturity. By age ten, coaches regularly pick the oldest and largest potential players for the more competitive “rep squads,” where the players will receive better coaching, have more practice time, and play many more games. By thirteen or fourteen, all of the extra experience and coaching will have actually made the players better, and they will be selected for the more competitive league(s). The same thing happens in American youth baseball and European soccer, but with different cutoff dates.

The phenomenon is also observable in education. Economists Kelly Bedard and Elizabeth Dhuey found that on math and science tests, the older children in fourth grade regularly score better than the youngest children. This can affect whether a child qualifies for a gifted program. When Bedard and Dhuey extended their analysis to four-year colleges, they found that the students who belonged to the relatively youngest group were underrepresented by more than 10 percent.

Section 5.

The top-level hockey players were given opportunities they neither deserved nor earned. Sociologist Robert Merton called this the “Matthew Effect,” after the verse in the Gospel of Matthew:

“For unto everyone that hath shall be given, and he shall have abundance. But from that hath not shall be taken away even that which he hath.”

The successful receive more resources: the best students receive the best teaching, the richest citizens get the biggest tax breaks, the largest kids get the best coaching. Sociologists call this “accumulative advantage.” Gladwell points out that cutoff dates exclude nearly half of the potential athletes from a population. Junior hockey teams in the Czech Republic show the same unbalanced distribution of birthdays as in Canada. If Canada or the Czech Republic separated each of their youth leagues into two separate leagues, one for kids born in the first half of the year, and one for kids born in the second half of the year, they would have twice as many athletes available for their national teams. Similarly, schools could separate kindergarten classes into students born in the first, middle, and last four months of the year. The benefits would justify the added administrative work, but, writes Gladwell, the scheme would run afoul of society’s need to believe that individual merit matters more than the rules society has created.

Section 6.

Gord Wasden, the father of one of the Canadian Hockey League boys from the first section, describes his son. Scott Wasden worked hard to get where he is, but he has also generally had the advantage of being big compared to others on his team. He was born on January 4.

Analysis: Introduction: The Roseto Mystery & Chapter 1: The Matthew Effect

Gladwell's thesis argues that that the idea of rugged, individual success is not accurate. Rather, the most successful person doesn’t thrive without some environmental and social influence plus a dose of good fortune.  After laying out the concepts of a meritocracy and suggesting that this is the way that hockey players advance in Canada, he immediately undercuts this idea. Gladwell uses the illustration of birthday distribution as an example of an invisible contributor to the success of hockey players. With a registration cutoff date of January 1, players born from January 2 through March 31 are older than teammates born later in the year. These older players are likely bigger, faster, more coordinated, and more mature. Since the older players are seen as more skilled, they get selected for more advanced leagues with more practice, more games, and higher-quality coaching. By the time these older players reach their early teens, the extra advantages gained from being judged better because of their birthday translate into being better players. Similarly, the age cutoff for school registrations often mistakes maturity for ability. As a result, the older children appear smarter, get put into advanced groups, and qualify for gifted programs. The birthdate bias carries through to college.

Advantages result in more advantages. Gladwell reinforces this idea with the “Matthew Effect,” which states that "success leads to more success." More simply: by being a little bit better, a hockey player will get opportunities that may result in the player becoming an outlier. Gladwell implies that the systems that determine success are not efficient. He asks readers to question the way we, as a society, think about success. He suggests that changing the systems in athletics and education would chip away at the myth of individual merit as the chief marker of success and help level the playing field. Gladwell's model for this phenomenon is hockey player Scott Wasden. By demonstrating that Scott had the passion, talent, and work ethic for the game, as well as the good luck to be born on January 4, Gladwell reasons that Wasden, like many others he will be profiling, benefit by being both good and lucky.

Reference

+ diff --git a/save/reading/outliers/2.html b/save/reading/outliers/2.html index e6c0de9b..19124639 100644 --- a/save/reading/outliers/2.html +++ b/save/reading/outliers/2.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Chapter Two: The 10,000-Hour Rule

Summary: Chapter Two: The 10,000-Hour Rule

Section 1.

Bill Joy, a co-founder of Sun Microsystems, is one of the most influential computer programmers of all time. Joy attended the University of Michigan, thinking to become a biologist or mathematician, but he became obsessed with the Computer Center that opened during his freshman year. In 1975, he enrolled in graduate school at UC Berkeley. At both schools, Bill Joy spent much of his free time programming. After graduating from Berkeley, he founded Sun Microsystems, eventually rewriting the Java programming language. He would appear to be a good example of success based on individual merit.

Section 2.

If achievement is the combination of talent and preparation, how much does innate talent affect one’s success? In the 1990s, a study at Berlin’s elite Academy of Music determined that, regardless of instrument, all of the world-class students had practiced more than 10,000 hours. They did not find anyone at the top level who spent less time, nor did they find anyone who spent that amount of time who was not successful. Neurologist Daniel Levitin states that, across many fields, world-class expertise is never accomplished in less than 10,000 hours. The law holds even for a prodigy like Mozart, who started composing at age six: he did not compose his first masterwork until he was twenty-one. The youth athletes from the previous chapter who made it to the professional level put in 10,000 hours of practice. And note: individuals cannot normally put in that much practice without help. Most people will need supportive parents, financial stability, and probably a special program—like an all-star youth hockey team.

Section 3.

Bill Joy was certainly intelligent, having achieved a perfect score on the math portion of his Scholastic Aptitude Test. His opportunities, however, were extraordinary. Bill Joy happened to choose a college that had a time-sharing computer available, something that was exceedingly rare during the early 1970s. While most students had to pay for computer time, Bill Joy exploited a bug in the college’s system to gain unlimited access to the Computer Center, which was walking distance from where he lived. He was able to spend almost all of his free time programming, and when he went to Berkeley, he had a terminal at home, where he could program until he fell asleep at his keyboard. Bill Joy was able to accumulate 10,000 hours while in college.

Section 4.

The Beatles are another example of the 10,000-hours principle. In 1960, when they were still a high school rock band, they were given the chance to travel to Hamburg, Germany and play in various strip clubs. The Beatles were contracted to play for hours every night, seven nights a week, and thereby were forced to develop as musicians. After a year and a half, they had performed 270 nights. By 1964, when they first found commercial success, they had performed an estimated twelve hundred times—more than most band bands do in an entire career.

Section 5.

Born in Seattle to affluent parents, Bill Gates was sent to a private school for seventh grade. The school’s Mother’s Club funded the purchase of a time-sharing terminal connected to a mainframe computer in Seattle. As an eighth-grader, Gates was able to start programming. When the Mother’s Club could no longer pay for computing time, Gates was able to continue programming at Information Sciences, Inc. (ISI) through a connection he made with one of the school parents. After that, one of ISI’s founders recommended Gates for a programming project at the Bonneville Power station. Gates was able to leave high school during his senior year to program for the Bonneville Power station as an independent study project. By the time Bill Gates dropped out of Harvard, he was well past 10,000 hours of experience.

Section 6.

In a list of the seventy-five richest people in human history, going as far back as ancient Egypt and converting all wealth estimates into modern U.S. dollars, fourteen names are Americans born within nine years of one another (including John D. Rockefeller and J.P. Morgan). What accounts for the fact that a list that covers thousands of years should have 20 percent of its members so close together? The fourteen Americans happened to live during the 1860s and 1870s, when the American economy was undergoing a huge transformation: the expansion of the railroads and the creation of Wall Street. Gladwell argues that the fourteen names are so close in birth date because they were all the perfect age to seize the opportunities available.

Bill Joy and Bill Gates were also born at just the right time. In 1975, Popular Electronics ran a cover story about the Altair 8800, a $397 microcomputer kit. Someone born before 1954 would likely already have a job with IBM, working on mainframes. Someone born after 1956 would likely still be in high school. Most of the biggest pioneers in the modern computer industry, including Bill Gates, Bill Joy, Steve Jobs, and Eric Schmidt, were born in 1954 or 1955, as were Joy’s three fellow founders at Sun.

Analysis: Chapter Two: The 10,000-Hour Rule

Gladwell introduces his controversial and widely disputed 10,000 hours rule. Simply put, the rule suggests that to master a skill, an individual needs to practice it for 10,000 hours. Gladwell argues that, like hockey, success in computing requires both skill and luck, rather than pure, simple, natural ability. Gladwell's example is situated at the University of Michigan, specifically the new computer center, in 1971. The story of Bill Joy undermines the idea of success as an inexplicable, miraculous accomplishment. Though Gladwell agrees Joy is bright and talented, Joy also lucks into several happy accidents that allow for increased access. These strokes of luck give Joy the opportunity to become a computer expert. Gladwell's use of a psychological study conducted at the Academy of Music in Berlin, Germany, in the early 1990s forms the crux of his argument in this chapter. However, critics have suggested that this study was flawed and that there is no incontrovertible evidence to suggest that doing anything for 10,000 hours guarantees mastery. Rather, practice is, as Gladwell points out elsewhere throughout the text, just one of the factors in success. However, he also correlates the familial and economic advantages necessary to reach 10,000 of practice time, reinforcing the larger thesis of the book.

Gladwell argues that the Beatles and Bill Gates are examples of his notion of time spent directly relating to mastery. While detailing how the Beatles reached the 10,000-hour threshold for mastery, Gladwell also highlights the lucky breaks they had in achieving success, like the connection that landed the band in Hamburg’s music scene. Additionally, while Gates has become something of an American folk hero, Gladwell argues that Gates did not reach his great achievements completely on his own. His wealthy family, his lucky interaction with a computer in 1968, and his college experience allowed him far greater access to opportunity. Without this combination of factors, along with his intelligence and drive, Gates would likely not have become a household name. Again, Gladwell reinforces the idea that success comes not only from being good, but from having no small amount of luck, whether that be time, money, or, in an echo of the hockey player example, birthdate.

Gladwell claims that one important factor of success is the year in which one is born. In terms of wealth, there are 14 Americans, born in a nine-year period of the 1800s, who are among the richest people in history. This suggests that there was some connection to when they were born and the opportunities available to them in terms of innovation and invention, as well as the position they were in to take advantage of the opportunities. Similarly, men born in the same era of Bill Gates were coming of age at the bleeding edge of technology. Proximity to social and technological change, as well as the wealth and connections to take advantage of it, put these men in an advantageous position. Being in the right place at the right time, Gladwell argues, has at least as much to do with success as one's inborn abilities.

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Chapter Two: The 10,000-Hour Rule

Summary: Chapter Two: The 10,000-Hour Rule

Section 1.

Bill Joy, a co-founder of Sun Microsystems, is one of the most influential computer programmers of all time. Joy attended the University of Michigan, thinking to become a biologist or mathematician, but he became obsessed with the Computer Center that opened during his freshman year. In 1975, he enrolled in graduate school at UC Berkeley. At both schools, Bill Joy spent much of his free time programming. After graduating from Berkeley, he founded Sun Microsystems, eventually rewriting the Java programming language. He would appear to be a good example of success based on individual merit.

Section 2.

If achievement is the combination of talent and preparation, how much does innate talent affect one’s success? In the 1990s, a study at Berlin’s elite Academy of Music determined that, regardless of instrument, all of the world-class students had practiced more than 10,000 hours. They did not find anyone at the top level who spent less time, nor did they find anyone who spent that amount of time who was not successful. Neurologist Daniel Levitin states that, across many fields, world-class expertise is never accomplished in less than 10,000 hours. The law holds even for a prodigy like Mozart, who started composing at age six: he did not compose his first masterwork until he was twenty-one. The youth athletes from the previous chapter who made it to the professional level put in 10,000 hours of practice. And note: individuals cannot normally put in that much practice without help. Most people will need supportive parents, financial stability, and probably a special program—like an all-star youth hockey team.

Section 3.

Bill Joy was certainly intelligent, having achieved a perfect score on the math portion of his Scholastic Aptitude Test. His opportunities, however, were extraordinary. Bill Joy happened to choose a college that had a time-sharing computer available, something that was exceedingly rare during the early 1970s. While most students had to pay for computer time, Bill Joy exploited a bug in the college’s system to gain unlimited access to the Computer Center, which was walking distance from where he lived. He was able to spend almost all of his free time programming, and when he went to Berkeley, he had a terminal at home, where he could program until he fell asleep at his keyboard. Bill Joy was able to accumulate 10,000 hours while in college.

Section 4.

The Beatles are another example of the 10,000-hours principle. In 1960, when they were still a high school rock band, they were given the chance to travel to Hamburg, Germany and play in various strip clubs. The Beatles were contracted to play for hours every night, seven nights a week, and thereby were forced to develop as musicians. After a year and a half, they had performed 270 nights. By 1964, when they first found commercial success, they had performed an estimated twelve hundred times—more than most band bands do in an entire career.

Section 5.

Born in Seattle to affluent parents, Bill Gates was sent to a private school for seventh grade. The school’s Mother’s Club funded the purchase of a time-sharing terminal connected to a mainframe computer in Seattle. As an eighth-grader, Gates was able to start programming. When the Mother’s Club could no longer pay for computing time, Gates was able to continue programming at Information Sciences, Inc. (ISI) through a connection he made with one of the school parents. After that, one of ISI’s founders recommended Gates for a programming project at the Bonneville Power station. Gates was able to leave high school during his senior year to program for the Bonneville Power station as an independent study project. By the time Bill Gates dropped out of Harvard, he was well past 10,000 hours of experience.

Section 6.

In a list of the seventy-five richest people in human history, going as far back as ancient Egypt and converting all wealth estimates into modern U.S. dollars, fourteen names are Americans born within nine years of one another (including John D. Rockefeller and J.P. Morgan). What accounts for the fact that a list that covers thousands of years should have 20 percent of its members so close together? The fourteen Americans happened to live during the 1860s and 1870s, when the American economy was undergoing a huge transformation: the expansion of the railroads and the creation of Wall Street. Gladwell argues that the fourteen names are so close in birth date because they were all the perfect age to seize the opportunities available.

Bill Joy and Bill Gates were also born at just the right time. In 1975, Popular Electronics ran a cover story about the Altair 8800, a $397 microcomputer kit. Someone born before 1954 would likely already have a job with IBM, working on mainframes. Someone born after 1956 would likely still be in high school. Most of the biggest pioneers in the modern computer industry, including Bill Gates, Bill Joy, Steve Jobs, and Eric Schmidt, were born in 1954 or 1955, as were Joy’s three fellow founders at Sun.

Analysis: Chapter Two: The 10,000-Hour Rule

Gladwell introduces his controversial and widely disputed 10,000 hours rule. Simply put, the rule suggests that to master a skill, an individual needs to practice it for 10,000 hours. Gladwell argues that, like hockey, success in computing requires both skill and luck, rather than pure, simple, natural ability. Gladwell's example is situated at the University of Michigan, specifically the new computer center, in 1971. The story of Bill Joy undermines the idea of success as an inexplicable, miraculous accomplishment. Though Gladwell agrees Joy is bright and talented, Joy also lucks into several happy accidents that allow for increased access. These strokes of luck give Joy the opportunity to become a computer expert. Gladwell's use of a psychological study conducted at the Academy of Music in Berlin, Germany, in the early 1990s forms the crux of his argument in this chapter. However, critics have suggested that this study was flawed and that there is no incontrovertible evidence to suggest that doing anything for 10,000 hours guarantees mastery. Rather, practice is, as Gladwell points out elsewhere throughout the text, just one of the factors in success. However, he also correlates the familial and economic advantages necessary to reach 10,000 of practice time, reinforcing the larger thesis of the book.

Gladwell argues that the Beatles and Bill Gates are examples of his notion of time spent directly relating to mastery. While detailing how the Beatles reached the 10,000-hour threshold for mastery, Gladwell also highlights the lucky breaks they had in achieving success, like the connection that landed the band in Hamburg’s music scene. Additionally, while Gates has become something of an American folk hero, Gladwell argues that Gates did not reach his great achievements completely on his own. His wealthy family, his lucky interaction with a computer in 1968, and his college experience allowed him far greater access to opportunity. Without this combination of factors, along with his intelligence and drive, Gates would likely not have become a household name. Again, Gladwell reinforces the idea that success comes not only from being good, but from having no small amount of luck, whether that be time, money, or, in an echo of the hockey player example, birthdate.

Gladwell claims that one important factor of success is the year in which one is born. In terms of wealth, there are 14 Americans, born in a nine-year period of the 1800s, who are among the richest people in history. This suggests that there was some connection to when they were born and the opportunities available to them in terms of innovation and invention, as well as the position they were in to take advantage of the opportunities. Similarly, men born in the same era of Bill Gates were coming of age at the bleeding edge of technology. Proximity to social and technological change, as well as the wealth and connections to take advantage of it, put these men in an advantageous position. Being in the right place at the right time, Gladwell argues, has at least as much to do with success as one's inborn abilities.

Reference

+ diff --git a/save/reading/outliers/3.html b/save/reading/outliers/3.html index 42b0b817..a1c6581c 100644 --- a/save/reading/outliers/3.html +++ b/save/reading/outliers/3.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Chapter 3: The Trouble with Geniuses, Part 1

Summary: Chapter Three: The Trouble with Geniuses, Part 1

Section 1.

Chris Langan appeared on the television trivia show 1 vs. 100 after being the subject of interviews and at least one documentary, due to his extremely high IQ. He had little difficulty in high school, got a perfect score on his SAT, and read through Principia Mathematica as a teenager. On 1 vs. 100, Langan cashed out with winnings of $250,000.

Section 2.

Shortly after World War I, Lewis Terman, creator of the widely used Stanford-Binet IQ test, became fascinated with child prodigies. In 1921, he identified exceptionally gifted 1,470 students who came to be known as the “Termites.” Terman kept track of them over the years, carefully cataloging their educational achievement, marriages, psychological health, and employment. Terman was sure that the Termites would be the future elite of the United States. The same confidence underlies the use of IQ-like tests, such as the SAT, to assess applicants at Ivy League schools and corporations such as Microsoft and Google. Gladwell states that Terman was wrong about the Termites, and if he had met Chris Langan as a teenager, he would have been wrong about him, too.

Section 3.

Gladwell gives two examples—one easy and one much harder—of questions that use visual puzzles to test IQ, without requiring any language abilities or specific factual knowledge. The average human will score 100. Those scoring below 70 are considered mentally disabled, and those who are successful in graduate programs likely have an IQ of 115 or higher. According to Gladwell, however, above 120 IQ makes little or no difference to success. A similar point applies to basketball: height is certainly an advantage, but there is, at best, modest value in being six foot seven instead of six foot six. A basketball player just needs to be tall enough.

A list of the last twenty-five Americans to win a Nobel Prize in Medicine includes graduates of prestigious schools, such as Columbia, Harvard, and MIT, but also graduates of DePauw, Holy Cross, and Gettysburg College. Similarly, there have been American Nobel laureates in Chemistry from Harvard and MIT, but also from Notre Dame and the University of Illinois. Harvard might have more intelligent students, but many other colleges have students smart enough to win a Nobel.

At the University of Michigan law school, around 10 percent of students are racial minorities. Without affirmative action, there would be less than 3 percent. Looking at career performance after graduation, Michigan found no difference between white and minority graduates. Minority students come into law school with weaker academic credentials than their white counterparts, but they are above the threshold required to be just as successful.

Section 4.

Not all questions that test for intelligence have a single correct answer. A different sort of question might ask for a list of different uses for a brick, or a blanket. A question like this measures imagination and creativity. At a top British high school, one student lists more than ten uses, many of which are comical. Another student, a prodigy with one of the school’s highest IQs, lists just a few uses, all of which are practical. Compared to an IQ test, asking about different uses for a brick might be a better way to identify future Nobel Prize winners.

Section 5.

Terman’s error was using intelligence alone to choose his Termites. While some of the Termites had successful careers, an unexpectedly high went on to careers that even Terman didn’t consider to be successful. The two students tested by Terman’s team who actually did go on to win Nobels were not selected as Termites: their IQs were too low. Terman eventually concluded that “intellect and achievement are far from perfectly correlated.”

Gladwell states that to understand Chris Langan’s prospects of becoming a “true outlier,” one must learn more about him.

Analysis: Chapter Three: The Trouble with Geniuses, Part 1

Intelligence, Gladwell argues, does not equal success. He dedicates this chapter to the examination of geniuses. Comparing the young subjects of Lewis Terman to Chris Langan, Gladwell argues against Terman’s idea that genius is a key to societal advancement. Gladwell lists Langan’s early accomplishments as a shining example of Terman's idea, then swiftly undercuts expectations. Gladwell argues again that individuals do not succeed or fail solely on their own, but rather due to a constellation of factors, many of which are uncontrollable. Langan's early achievements would suggest great things and a continued path toward accomplishment, but Gladwell includes the anecdote of his game show appearance to undermine the notion that genius equals success. Using two questions from an IQ test, Gladwell introduces the idea of an IQ threshold to examine the the larger notion of intelligence and its limitations. Arguing that the measure of someone’s intelligence is only helpful up to a point, Gladwell uses examples of schools that Nobel laureates attended for undergraduate studies. Some, he points out, are elite institutions; others are not. Additionally, he points to success among graduates of the law school at the University of Michigan. There was no quantifiable difference in success post-graduation between white and POC students, some of whom were admitted under affirmative action with slightly lower undergraduate grades and standardized test scores. Reasonably, then, the level of intelligence beyond a certain point is moot. All of the students were intelligent enough to graduate, and beyond that, he argues, their intelligence predicted nothing.

Elements other than intelligence must contribute to success. Gladwell expands on his notion of an intelligence threshold and examines these other factors through an example of a question on a divergence test. Using examples of two students at an elite British school, Gladwell shows that the divergence test has no right answers, but instead looks for answers that demonstrate uniqueness and creativity. Intelligence matters, but so does imagination, creativity, and outside-the-box thinking. Gladwell circles back to Terman, reinforcing that the error when choosing his Termites was a focus on intelligence alone. He once again turns his attention to Chris Langan, foreshadowing that Langan’s story did not follow a direct line to achievement. Intelligence alone does not offer a certain path to success.

Reference

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Chapter 3: The Trouble with Geniuses, Part 1

Summary: Chapter Three: The Trouble with Geniuses, Part 1

Section 1.

Chris Langan appeared on the television trivia show 1 vs. 100 after being the subject of interviews and at least one documentary, due to his extremely high IQ. He had little difficulty in high school, got a perfect score on his SAT, and read through Principia Mathematica as a teenager. On 1 vs. 100, Langan cashed out with winnings of $250,000.

Section 2.

Shortly after World War I, Lewis Terman, creator of the widely used Stanford-Binet IQ test, became fascinated with child prodigies. In 1921, he identified exceptionally gifted 1,470 students who came to be known as the “Termites.” Terman kept track of them over the years, carefully cataloging their educational achievement, marriages, psychological health, and employment. Terman was sure that the Termites would be the future elite of the United States. The same confidence underlies the use of IQ-like tests, such as the SAT, to assess applicants at Ivy League schools and corporations such as Microsoft and Google. Gladwell states that Terman was wrong about the Termites, and if he had met Chris Langan as a teenager, he would have been wrong about him, too.

Section 3.

Gladwell gives two examples—one easy and one much harder—of questions that use visual puzzles to test IQ, without requiring any language abilities or specific factual knowledge. The average human will score 100. Those scoring below 70 are considered mentally disabled, and those who are successful in graduate programs likely have an IQ of 115 or higher. According to Gladwell, however, above 120 IQ makes little or no difference to success. A similar point applies to basketball: height is certainly an advantage, but there is, at best, modest value in being six foot seven instead of six foot six. A basketball player just needs to be tall enough.

A list of the last twenty-five Americans to win a Nobel Prize in Medicine includes graduates of prestigious schools, such as Columbia, Harvard, and MIT, but also graduates of DePauw, Holy Cross, and Gettysburg College. Similarly, there have been American Nobel laureates in Chemistry from Harvard and MIT, but also from Notre Dame and the University of Illinois. Harvard might have more intelligent students, but many other colleges have students smart enough to win a Nobel.

At the University of Michigan law school, around 10 percent of students are racial minorities. Without affirmative action, there would be less than 3 percent. Looking at career performance after graduation, Michigan found no difference between white and minority graduates. Minority students come into law school with weaker academic credentials than their white counterparts, but they are above the threshold required to be just as successful.

Section 4.

Not all questions that test for intelligence have a single correct answer. A different sort of question might ask for a list of different uses for a brick, or a blanket. A question like this measures imagination and creativity. At a top British high school, one student lists more than ten uses, many of which are comical. Another student, a prodigy with one of the school’s highest IQs, lists just a few uses, all of which are practical. Compared to an IQ test, asking about different uses for a brick might be a better way to identify future Nobel Prize winners.

Section 5.

Terman’s error was using intelligence alone to choose his Termites. While some of the Termites had successful careers, an unexpectedly high went on to careers that even Terman didn’t consider to be successful. The two students tested by Terman’s team who actually did go on to win Nobels were not selected as Termites: their IQs were too low. Terman eventually concluded that “intellect and achievement are far from perfectly correlated.”

Gladwell states that to understand Chris Langan’s prospects of becoming a “true outlier,” one must learn more about him.

Analysis: Chapter Three: The Trouble with Geniuses, Part 1

Intelligence, Gladwell argues, does not equal success. He dedicates this chapter to the examination of geniuses. Comparing the young subjects of Lewis Terman to Chris Langan, Gladwell argues against Terman’s idea that genius is a key to societal advancement. Gladwell lists Langan’s early accomplishments as a shining example of Terman's idea, then swiftly undercuts expectations. Gladwell argues again that individuals do not succeed or fail solely on their own, but rather due to a constellation of factors, many of which are uncontrollable. Langan's early achievements would suggest great things and a continued path toward accomplishment, but Gladwell includes the anecdote of his game show appearance to undermine the notion that genius equals success. Using two questions from an IQ test, Gladwell introduces the idea of an IQ threshold to examine the the larger notion of intelligence and its limitations. Arguing that the measure of someone’s intelligence is only helpful up to a point, Gladwell uses examples of schools that Nobel laureates attended for undergraduate studies. Some, he points out, are elite institutions; others are not. Additionally, he points to success among graduates of the law school at the University of Michigan. There was no quantifiable difference in success post-graduation between white and POC students, some of whom were admitted under affirmative action with slightly lower undergraduate grades and standardized test scores. Reasonably, then, the level of intelligence beyond a certain point is moot. All of the students were intelligent enough to graduate, and beyond that, he argues, their intelligence predicted nothing.

Elements other than intelligence must contribute to success. Gladwell expands on his notion of an intelligence threshold and examines these other factors through an example of a question on a divergence test. Using examples of two students at an elite British school, Gladwell shows that the divergence test has no right answers, but instead looks for answers that demonstrate uniqueness and creativity. Intelligence matters, but so does imagination, creativity, and outside-the-box thinking. Gladwell circles back to Terman, reinforcing that the error when choosing his Termites was a focus on intelligence alone. He once again turns his attention to Chris Langan, foreshadowing that Langan’s story did not follow a direct line to achievement. Intelligence alone does not offer a certain path to success.

Reference

+ diff --git a/save/reading/outliers/4.html b/save/reading/outliers/4.html index ff78d8cb..37e626cf 100644 --- a/save/reading/outliers/4.html +++ b/save/reading/outliers/4.html @@ -8,7 +8,7 @@ - + @@ -30,8 +30,8 @@ -
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Chapter 4: The Trouble with Geniuses, Part 2

Summary: Chapter Four: The Trouble with Geniuses, Part 2

Section 1.

Chris Langan’s mother had four children, all from different fathers. Her first husband died in Mexico, the second was murdered, the third committed suicide, and the fourth was an abusive alcoholic. Langan says he has never met someone who grew up as impoverished as he and his brothers did. Attending Reed College, in Oregon, on a scholarship, he felt as though he did not belong with the rest of the students. When his mother neglected to fill out the financial aid forms, he lost his scholarship and dropped out. According to Langan, the school just did not care about their students. Later, Langan attended Montana State University in Bozeman but he dropped out when a dean refused Langan’s request to adjust his class schedule because of car trouble. He still has intellectual interests and has been working on a treatise called the “Cognitive Theoretic Model of the Universe.” When asked if, hypothetically, he would take a position at Harvard, he acknowledges the benefit of an environment with so much intellectual energy, but he worries about a lack of intellectual freedom.

Section 2.

Gladwell points out the oddity of Langan’s experiences. Most colleges, especially small ones, try to accommodate student needs. Smart people take positions at places like Harvard instead of in the private sector precisely for the added intellectual freedom. Gladwell contrasts Langan’s story with Robert Oppenheimer’s. While at Cambridge, Oppenheimer became frustrated with his tutor and tried to poison him. After negotiations with the school administration, Oppenheimer was put on probation and assigned to a psychiatrist. Whereas Langan dropped out after his mother failed to fill out paperwork, Oppenheimer managed to stay in college after trying to kill someone. Later, Oppenheimer convinced General Leslie Groves to make Oppenheimer the scientific director of the Manhattan Project. Oppenheimer had the ability to persuade people, where Langan did not.

Section 3.

Psychologist Robert Sternberg calls the ability to persuade someone “practical intelligence.” It involves knowing what to say, how to say it, and when. It requires an ability to read situations. Individuals can have either practical or analytical intelligence, or in the case of Oppenheimer, both. To understand where one obtains practical intelligence, Gladwell refers to a study conducted by Annette Lareau.

Lareau observed parenting strategies in both Black and white families from different socioeconomic strata. She found two distinct strategies: “concerted cultivation” and “accomplishment of natural growth.” Concerted cultivation, most common in middle-class and wealthier families, is defined by parents’ active promotion of their children’s talents and interests. Accomplishment of natural growth, most common in working-class or impoverished families, is defined by parents’ lack of interest or interaction in their children’s free time. Concerted cultivation, writes Gladwell, encourages children to seek opportunities for growth and to advocate for themselves. Accomplishment of natural growth leaves children unprepared to shape their environment for their own benefit. Concerted cultivation fosters an attitude better suited for success in the modern world.

Section 4.

Oppenheimer was raised by affluent parents who sent him to a progressive private school and took an active interest in his hobbies.

  • Affluent: Having an abundant supply of money or possessions of value.

By contrast, Chris Langan’s brother Mark states that as children, they learned to resent authority. Mark, too, was unable to obtain financial aid, because he had no knowledge of how the system worked. If Chris Langan had been raised in a family that valued education, he probably would have had more success.

Section 5.

Once the Termites reached working adulthood, Terman grouped 730 of the males into three categories, based on their levels of success. The top 20 percent were upper-class professionals, while the bottom 20 percent had low-paying jobs or were unemployed. After analyzing the differences between the groups, Terman found that the bottom 20 percent came almost entirely from the lowest social and economic classes. What they lacked was “a community around them that prepared them properly for the world.”

Section 6.

Chris Langan lives on a horse farm in Missouri, where he still writes. He is happily married and continues to read physics and philosophy. While he has spent decades on his writing, almost none of it has ever been published. Langan admits he has not tried to contact publishers or found an agent—and does not plan to. Chris Langan did not have the support necessary to meet success. Gladwell points that no one ever makes it alone, regardless of if they are successful musicians, athletes, tech billionaires, or geniuses.

Analysis: Chapter Four: The Trouble with Geniuses, Part 2

Family background plays a crucial role in an individual’s success. While a genius like Chris Langan should thrive on a college campus, he drops out. Langan doesn’t struggle with academics, but with paperwork, procedures, and environment. Gladwell’s characterization of Langan almost makes him seem like two separate characters: a confident, genius game show contestant versus a child from a poor and troubled family. Langan may be a true outlier in the sense that he doesn’t seem to fit in academia or the working-class world.  Langan’s story is ironic. His brilliant mind should propel him to success. However, his story also perfectly proves Gladwell’s point that brainpower alone does not lead to success. The author delves deeper into the irony of Langan’s situation by comparing him to Robert Oppenheimer, who worked on the nuclear bomb during World War II. Like Langan, Oppenheimer possesses great intelligence. Unlike Langan, Oppenheimer has an understanding that allows him to navigate the world effectively. Oppenheimer knows how to combat challenges, where Langan gets bested by a financial aid problem and class schedule. Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority. Without a family background that encourages success, intelligence is not enough.

Contrast & Comparison

Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority.

The power of persuasion is an important factor that drives success. Gladwell notes that the power of persuasion is practical intelligence. He contrasts practical intelligence with analytical ability, noting that just because a person is smart does not mean they have practical intelligence. These two types of knowledge are not necessarily coeval. He reinforces this point with a return to the comparison of Langan and Oppenheimer. Both men are exceedingly intelligent, but Langan lacks the social savvy of practical intelligence. Gladwell suggests that individuals gain practical intelligence skills from their families, discussing a study by sociologist Annette Lareau to prove his point. Children from wealthier families learn how to interact with society in a way that drives achievement. Successful people have the power of persuasion and can convince others to see things from their point of view.

Success, then, depends on more than individual effort. Gladwell builds this argument by detailing the differences between Oppenheimer’s upbringing and Langan’s. Oppenheimer lived in an upper-class neighborhood with myriad advantages. He learned how to negotiate and stand up for himself. Langan’s family moved from place to place, struggling for jobs, money, food, and clothes, and Langan learned that he couldn’t rely on others. Gladwell's consideration of the Termites' success or struggles as adults supports his assertion that success is more than an individual effort; Gladwell states, “In the end, only one thing mattered: family background.” Terman’s findings and Gladwell’s conclusion do not mean that talented individuals from lower social and economic classes cannot have successful futures. To succeed, everyone needs help along the way, if not from family, then from a supportive community. Individuals do not achieve success solely on their own.

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Chapter 4: The Trouble with Geniuses, Part 2

Summary: Chapter Four: The Trouble with Geniuses, Part 2

Section 1.

Chris Langan’s mother had four children, all from different fathers. Her first husband died in Mexico, the second was murdered, the third committed suicide, and the fourth was an abusive alcoholic. Langan says he has never met someone who grew up as impoverished as he and his brothers did. Attending Reed College, in Oregon, on a scholarship, he felt as though he did not belong with the rest of the students. When his mother neglected to fill out the financial aid forms, he lost his scholarship and dropped out. According to Langan, the school just did not care about their students. Later, Langan attended Montana State University in Bozeman but he dropped out when a dean refused Langan’s request to adjust his class schedule because of car trouble. He still has intellectual interests and has been working on a treatise called the “Cognitive Theoretic Model of the Universe.” When asked if, hypothetically, he would take a position at Harvard, he acknowledges the benefit of an environment with so much intellectual energy, but he worries about a lack of intellectual freedom.

Section 2.

Gladwell points out the oddity of Langan’s experiences. Most colleges, especially small ones, try to accommodate student needs. Smart people take positions at places like Harvard instead of in the private sector precisely for the added intellectual freedom. Gladwell contrasts Langan’s story with Robert Oppenheimer’s. While at Cambridge, Oppenheimer became frustrated with his tutor and tried to poison him. After negotiations with the school administration, Oppenheimer was put on probation and assigned to a psychiatrist. Whereas Langan dropped out after his mother failed to fill out paperwork, Oppenheimer managed to stay in college after trying to kill someone. Later, Oppenheimer convinced General Leslie Groves to make Oppenheimer the scientific director of the Manhattan Project. Oppenheimer had the ability to persuade people, where Langan did not.

Section 3.

Psychologist Robert Sternberg calls the ability to persuade someone “practical intelligence.” It involves knowing what to say, how to say it, and when. It requires an ability to read situations. Individuals can have either practical or analytical intelligence, or in the case of Oppenheimer, both. To understand where one obtains practical intelligence, Gladwell refers to a study conducted by Annette Lareau.

Lareau observed parenting strategies in both Black and white families from different socioeconomic strata. She found two distinct strategies: “concerted cultivation” and “accomplishment of natural growth.” Concerted cultivation, most common in middle-class and wealthier families, is defined by parents’ active promotion of their children’s talents and interests. Accomplishment of natural growth, most common in working-class or impoverished families, is defined by parents’ lack of interest or interaction in their children’s free time. Concerted cultivation, writes Gladwell, encourages children to seek opportunities for growth and to advocate for themselves. Accomplishment of natural growth leaves children unprepared to shape their environment for their own benefit. Concerted cultivation fosters an attitude better suited for success in the modern world.

Section 4.

Oppenheimer was raised by affluent parents who sent him to a progressive private school and took an active interest in his hobbies.

  • Affluent: Having an abundant supply of money or possessions of value.

By contrast, Chris Langan’s brother Mark states that as children, they learned to resent authority. Mark, too, was unable to obtain financial aid, because he had no knowledge of how the system worked. If Chris Langan had been raised in a family that valued education, he probably would have had more success.

Section 5.

Once the Termites reached working adulthood, Terman grouped 730 of the males into three categories, based on their levels of success. The top 20 percent were upper-class professionals, while the bottom 20 percent had low-paying jobs or were unemployed. After analyzing the differences between the groups, Terman found that the bottom 20 percent came almost entirely from the lowest social and economic classes. What they lacked was “a community around them that prepared them properly for the world.”

Section 6.

Chris Langan lives on a horse farm in Missouri, where he still writes. He is happily married and continues to read physics and philosophy. While he has spent decades on his writing, almost none of it has ever been published. Langan admits he has not tried to contact publishers or found an agent—and does not plan to. Chris Langan did not have the support necessary to meet success. Gladwell points that no one ever makes it alone, regardless of if they are successful musicians, athletes, tech billionaires, or geniuses.

Analysis: Chapter Four: The Trouble with Geniuses, Part 2

Family background plays a crucial role in an individual’s success. While a genius like Chris Langan should thrive on a college campus, he drops out. Langan doesn’t struggle with academics, but with paperwork, procedures, and environment. Gladwell’s characterization of Langan almost makes him seem like two separate characters: a confident, genius game show contestant versus a child from a poor and troubled family. Langan may be a true outlier in the sense that he doesn’t seem to fit in academia or the working-class world.  Langan’s story is ironic. His brilliant mind should propel him to success. However, his story also perfectly proves Gladwell’s point that brainpower alone does not lead to success. The author delves deeper into the irony of Langan’s situation by comparing him to Robert Oppenheimer, who worked on the nuclear bomb during World War II. Like Langan, Oppenheimer possesses great intelligence. Unlike Langan, Oppenheimer has an understanding that allows him to navigate the world effectively. Oppenheimer knows how to combat challenges, where Langan gets bested by a financial aid problem and class schedule. Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority. Without a family background that encourages success, intelligence is not enough.

Contrast & Comparison

Oppenheimer’s family background gave him the confidence to deal with authority while Langan’s upbringing created a distrust of authority.

The power of persuasion is an important factor that drives success. Gladwell notes that the power of persuasion is practical intelligence. He contrasts practical intelligence with analytical ability, noting that just because a person is smart does not mean they have practical intelligence. These two types of knowledge are not necessarily coeval. He reinforces this point with a return to the comparison of Langan and Oppenheimer. Both men are exceedingly intelligent, but Langan lacks the social savvy of practical intelligence. Gladwell suggests that individuals gain practical intelligence skills from their families, discussing a study by sociologist Annette Lareau to prove his point. Children from wealthier families learn how to interact with society in a way that drives achievement. Successful people have the power of persuasion and can convince others to see things from their point of view.

Success, then, depends on more than individual effort. Gladwell builds this argument by detailing the differences between Oppenheimer’s upbringing and Langan’s. Oppenheimer lived in an upper-class neighborhood with myriad advantages. He learned how to negotiate and stand up for himself. Langan’s family moved from place to place, struggling for jobs, money, food, and clothes, and Langan learned that he couldn’t rely on others. Gladwell's consideration of the Termites' success or struggles as adults supports his assertion that success is more than an individual effort; Gladwell states, “In the end, only one thing mattered: family background.” Terman’s findings and Gladwell’s conclusion do not mean that talented individuals from lower social and economic classes cannot have successful futures. To succeed, everyone needs help along the way, if not from family, then from a supportive community. Individuals do not achieve success solely on their own.

Reference

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