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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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Presentation Problem 2-20

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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Welcome to Literature

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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

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Welcome to Physics

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 1

1: æ•°ć­Š

1.1: Taylor 汕開

  1. Taylor ć±•é–‹ïŒˆă‚ąăƒă‚Šăƒˆă«ćˆ‡ă‚ŠæšăŠă‚‹:

    F(x)=F(x0)+∑F(n)(x0)(x−x0)n/nF(x)=F\left(x_{0}\right)+\sum F^{(n)}\left(x_{0}\right)\left(x-x_{0}\right)^{n} / n

    ç·šćœąèż‘äŒŒïŒˆç‰č戄ăȘć ŽćˆïŒ‰:

    F(x)≈F(x0)+Fâ€Č(x0)(x−x0)F(x) \approx F\left(x_{0}\right)+F^{\prime}\left(x_{0}\right)\left(x-x_{0}\right)

    ∣x∣â‰Ș1|x| \ll 1 ăźăšăăźäŸ‹ ::

    sin⁡x≈x,cos⁡x≈1−x2/2,ex≈1+x\sin x \approx x, \cos x \approx 1-x^{2} / 2, e^{x} \approx 1+x

    ln⁡(1+x)≈x,(1+x)n≈1+nx\ln (1+x) \approx x,(1+x)^{n} \approx 1+n x

1.2: æ‘‚ć‹•æł•

  1. æ‘‚ć‹•æł•ïŒšæ‘‚ć‹•ăźăȘă„ïŒˆç›ŽæŽ„è§Łă‘ă‚‹ïŒ‰ć•éĄŒăźè§Łă‚’ 00 ç•Șç›źăźèż‘äŒŒć€€ăšă—ăŠæ±‚ă‚ïŒŒć‰ăźäŒŒć€€ă«ćŸșă„ăæŹĄăźèż‘äŒŒć€€ăźèŁœæ­Łă‚’çč°ă‚Šèż”ă—ăŠè§Łă‚’æ±‚ă‚ă‚‹ïŒŽ

1.3: ćźšæ•°äż‚æ•°ç·šćœąćŸźćˆ†æ–čçš‹ćŒ

  1. ćźšæ•°äż‚æ•°ç·šćœąćŸźćˆ†æ–čçš‹ćŒ ayâ€Čâ€Č+byâ€Č+cy=0a y^{\prime \prime}+b y^{\prime}+c y=0 ăźè§Ł:

    y=Aexp⁥(λ1x)+Bexp⁥(λ2x). y=A \exp \left(\lambda_1 x\right)+B \exp \left(\lambda_2 x\right) \text {. }

    ここで λ1,2\lambda_{1,2} はç‰č性æ–čçš‹ćŒ aλ2+bλ+c=0a \lambda^2+b \lambda+c=0 ぼ異ăȘ る 2 è§Ł. もし a,b,ca, b, c ăŒćźŸæ•°ă§ç‰č性æ–čçš‹ćŒăźè§ŁăŒè€‡çŽ æ•° λ1,2=γ±iω\lambda_{1,2}=\gamma \pm i \omega ăȘらば,

    y=CeÎłxsin⁥(ωx+φ0)y=C e^{\gamma x} \sin \left(\omega x+\varphi_0\right)

1.4: 耇玠数

  1. 耇玠数

    z=a+bi=∣z∣eiφ,zˉ=a−bi=∣z∣e−iÏ†âˆŁz∣2=zzˉ=a2+b2,φ=arg⁥z=arcsin⁥b∣z∣Re⁥z=(z+zˉ)/2,Im⁥z=(z−zˉ)/2i∣z1z2∣=∣z1∣∣z2∣,arg⁥z1z2=arg⁥z1+arg⁥z2eiφ=cosâĄÏ†+isinâĄÏ†cosâĄÏ†=eiφ+e−iφ2,sinâĄÏ†=eiφ−e−iφ2i\begin{gathered} z=a+b i=|z| e^{i \varphi}, \bar{z}=a-b i=|z| e^{-i \varphi} \\ |z|^2=z \bar{z}=a^2+b^2, \varphi=\arg z=\arcsin \frac{b}{|z|} \\ \operatorname{Re} z=(z+\bar{z}) / 2, \operatorname{Im} z=(z-\bar{z}) / 2 i \\ \left|z_1 z_2\right|=\left|z_1\right|\left|z_2\right|, \arg z_1 z_2=\arg z_1+\arg z_2 \\ e^{i \varphi}=\cos \varphi+i \sin \varphi \\ \cos \varphi=\frac{e^{i \varphi}+e^{-i \varphi}}{2}, \sin \varphi=\frac{e^{i \varphi}-e^{-i \varphi}}{2 i} \end{gathered}

1.5: ăƒ™ă‚Żăƒˆăƒ«ăźć†…ç©ăšć€–ç©

  1. ăƒ™ă‚Żăƒˆăƒ«ăźć†…ç©ăšć€–ç©ăŻćˆ†é…æł•ć‰‡ăŒæˆç«‹ă™ă‚‹ : a(b+c)=ab+aca(b+c)=a b+a c

    a⋅b=b⋅a=axbx+ayby+⋯=abcosâĄÏ†âˆŁa×b∣=absinâĄÏ†,a×b=−b×a⊄a,ba×b=(aybz−azby)ex+(azbx−axbz)ey+⋯a×[b×c]=(a⋅c)b−(a⋅b)c\begin{gathered} \boldsymbol{a} \cdot \boldsymbol{b}=\boldsymbol{b} \cdot \boldsymbol{a}=a_x b_x+a_y b_y+\cdots=a b \cos \varphi \\ |\boldsymbol{a} \times \boldsymbol{b}|=a b \sin \varphi, \boldsymbol{a} \times \boldsymbol{b}=-\boldsymbol{b} \times \boldsymbol{a} \perp \boldsymbol{a}, \boldsymbol{b} \\ \boldsymbol{a} \times \boldsymbol{b}=\left(a_y b_z-a_z b_y\right) \boldsymbol{e}_x+\left(a_z b_x-a_x b_z\right) \boldsymbol{e}_y+\cdots \\ \boldsymbol{a} \times[\boldsymbol{b} \times \boldsymbol{c}]=(\boldsymbol{a} \cdot \boldsymbol{c}) \boldsymbol{b}-(\boldsymbol{a} \cdot \boldsymbol{b}) \boldsymbol{c} \end{gathered}

    ă‚čă‚«ăƒ©ăƒŒäž‰é‡ç©ïŒˆ3 ă€ăźăƒ™ă‚Żăƒˆăƒ«ă§ćŒ”ă‚‰ă‚Œă‚‹ćčłèĄŒć››éą äœ“ăźäœ“ç©ïŒ‰:

    (a,b,c)≡a⋅[b×c]=[a×b]⋅c=(b,c,a)(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \equiv \boldsymbol{a} \cdot[\boldsymbol{b} \times \boldsymbol{c}]=[\boldsymbol{a} \times \boldsymbol{b}] \cdot \boldsymbol{c}=(\boldsymbol{b}, \boldsymbol{c}, \boldsymbol{a})

1.6: äœ™ćŒŠćźšç†ăšæ­ŁćŒŠćźšç†

  1. äœ™ćŒŠćźšç†ăšæ­ŁćŒŠćźšç†ïŒš

    c2=a2+b2−2abcos⁡Ca/sin⁡A=b/sin⁡B=2R\begin{aligned} & c^2=a^2+b^2-2 a b \cos C \\ & a / \sin A=b / \sin B=2 R \end{aligned}

1.7: äž‰è§’æł•

  1. sin⁥(α±ÎČ)=sin⁥αcos⁥Îȱcos⁥αsin⁥ÎČcos⁥(α±ÎČ)=cos⁥αcos⁥ÎČ∓sin⁥αsin⁥ÎČtan⁥(α±ÎČ)=(tan⁥α±tan⁥ÎČ)/(1∓tan⁥αtan⁥ÎČ)cos⁥2α=1+cos⁥2α2,sin⁥2α=1−cos⁥2α2cos⁥αcos⁥ÎČ=cos⁥(α+ÎČ)+cos⁥(α−ÎČ)2,
cos⁥α+cos⁥ÎČ=2(cos⁥α+ÎČ2+cosâĄÎ±âˆ’ÎČ2),
\begin{aligned} & \sin (\alpha \pm \beta)=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta \\ & \cos (\alpha \pm \beta)=\cos \alpha \cos \beta \mp \sin \alpha \sin \beta \\ & \tan (\alpha \pm \beta)=(\tan \alpha \pm \tan \beta) /(1 \mp \tan \alpha \tan \beta) \\ & \cos ^2 \alpha=\frac{1+\cos 2 \alpha}{2}, \sin ^2 \alpha=\frac{1-\cos 2 \alpha}{2} \\ & \cos \alpha \cos \beta=\frac{\cos (\alpha+\beta)+\cos (\alpha-\beta)}{2}, \ldots \\ & \cos \alpha+\cos \beta=2\left(\cos \frac{\alpha+\beta}{2}+\cos \frac{\alpha-\beta}{2}\right), \ldots \end{aligned}

1.8: ć††ć‘šè§’

  1. ć††ć‘šè§’ăŻäž­ćżƒè§’ăźćŠćˆ†. ă‚ˆăŁăŠïŒŒç›Žè§’äž‰è§’ćœąăźæ–œèŸșは ăăźć€–æŽ„ć††ăźç›ŽćŸ„. ă‚‚ă—ć››è§’ćœąăźćŻŸè§’ăźć’ŒăŒ 180 ćșŠăȘ ă‚‰ă°ïŒŒăă‚ŒăŻć††ă«ć†…æŽ„ă™ă‚‹.

1.9: äž‰è§’ćœąăźéąæš

  1. äž‰è§’ćœąăźéąæš =12aha=pr=p(p−a)(p−b)(p−c)=abc/4R=\frac{1}{2} a h_a=p r=\sqrt{p(p-a)(p-b)(p-c)}=a b c / 4 R

1.10: 重濃

  1. äž‰è§’ćœąăźé‡ćżƒăŻïŒŒäž­ç·šăźäș€ç‚čă§ïŒŒäž­ç·šă‚’ 2:1 ă«ć†…ćˆ†ă™ă‚‹.\

1.11: ăƒ™ă‚Żăƒˆăƒ«ă‚ąăƒ—ăƒ­ăƒŒăƒ supplemental

  1. ćčŸäœ•ăźć•éĄŒăžăźăƒ™ă‚Żăƒˆăƒ«ă‚ąăƒ—ăƒ­ăƒŒăƒ.

1.12: ćŸźćˆ†

  1. ćŸźćˆ†:

    (fg)â€Č=fâ€Čg+fgâ€Č,f[g(x)]â€Č=fâ€Č[g(x)]gâ€Č(x)(sin⁥x)â€Č=cos⁥x,(cos⁥x)â€Č=−sin⁥x(ex)â€Č=ex,(ln⁥x)â€Č=1/x,(xn)â€Č=nxn−1(arctan⁥x)â€Č=1/(1+x2)(arcsin⁥x)â€Č=−(arccos⁥x)â€Č=1/1−x2\begin{gathered} (f g)^{\prime}=f^{\prime} g+f g^{\prime}, f[g(x)]^{\prime}=f^{\prime}[g(x)] g^{\prime}(x) \\ (\sin x)^{\prime}=\cos x,(\cos x)^{\prime}=-\sin x \\ \left(e^x\right)^{\prime}=e^x,(\ln x)^{\prime}=1 / x,\left(x^n\right)^{\prime}=n x^{n-1} \\ (\arctan x)^{\prime}=1 /\left(1+x^2\right) \\ (\arcsin x)^{\prime}=-(\arccos x)^{\prime}=1 / \sqrt{1-x^2} \end{gathered}

1.13: ç©ćˆ†

  1. ç©ćˆ†ïŒšćŸźćˆ†ăźć…ŹćŒăźć·ŠèŸșべ揳èŸșă‚’ć…„ă‚Œæ›żăˆăŸă‚‚ăźăšćŒ ă˜ïŒˆé€†æŒ”çź—ïŒ‰.äŸ‹ăˆă°,

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

    çœźæ›ç©ćˆ†ăźç‰č戄ăȘ栎搈 :

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

1.14: 憆錐æ›Č線

  1. 憆錐æ›Č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} ăȘらば憆, a11(a11a22−a122)>0a_{11}\left(a_{11} a_{22}-a_{12}^2\right)>0 ăȘă‚‰ă°æ„•ć††, ⋯<0\cdots<0 ăȘらば揌æ›Č線, a11a22−a122=0a_{11} a_{22}-a_{12}^2=0 ăȘă‚‰ă°æ”Ÿç‰©ç·š. æ„•ć†† : l1+l2=2a,α1=α2l_1+l_2=2 a, \alpha_1=\alpha_2 [èšł è€…æłš : 焩ç‚čずæ›Č線䞊たç‚čă‚’ç”ă¶ç›Žç·šăšæŽ„ç·šăšăźăȘă™è§’ ], A=πabA=\pi a b. 揌æ›Č線 : l1−l2=2a,α1+α2=0l_1-l_2=2 a, \alpha_1+\alpha_2=0. 攟物線 :l+h=: l+h= const., α1=α2\alpha_1=\alpha_2.

1.15: æ•°ć€Œèšˆçź— & ć°ćœąèŠć‰‡

  1. æ•°ć€Œèšˆçź—. f(x)=0f(x)=0 ăźè§Łă‚’æ±‚ă‚ă‚‹ăƒ‹ăƒ„ăƒŒăƒˆăƒłæł• :

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

    èż‘äŒŒç©ćˆ†ăźć°ćœąèŠć‰‡ïŒš

    ∫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: ăƒ™ă‚Żăƒˆăƒ«ăźćŸźćˆ† & ç©ćˆ†

  1. ăƒ™ă‚Żăƒˆăƒ«ăźćŸźćˆ†ăšç©ćˆ†ïŒšæˆćˆ†ă”ăšă«ćŸźćˆ†/ç©ćˆ†ă™ă‚‹ïŒŽă‚ă‚‹ă„ăŻç„Ąé™ă«èż‘ă„22ă€ăźăƒ™ă‚Żăƒˆăƒ«ăźć·źă‚’æ±‚ă‚ă‚‹ă“ăšă§ ćŸźćˆ†ă™.
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/10.html b/academic/physics/ipho-formulas-jpn/10.html new file mode 100644 index 00000000..3f90ac10 --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/10.html @@ -0,0 +1,58 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 10 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 10

10: 熱抛歊

10.1: pV=wMRTp V=\frac{w}{M} R T

  1. pV=wMRTp V=\frac{w}{M} R T.

10.2: ăƒąăƒ«ăźæ°—äœ“ăźć†…éƒšă‚šăƒăƒ«ă‚źăƒŒ

  1. 1 ăƒąăƒ«ăźæ°—äœ“ăźć†…éƒšă‚šăƒăƒ«ă‚źăƒŒ: U=i2RTU=\frac{i}{2} R T [èšłè€…æłš: 捘 ćŽŸć­ćˆ†ć­ç†æƒłæ°—äœ“ i=3i=3, äșŒćŽŸć­ćˆ†ć­ç†æƒłæ°—䜓 i=5]i=5].

10.3: æš™æș–状態

  1. æš™æș–çŠ¶æ…‹ă§ăź 1 ăƒąăƒ«ăźæ°—äœ“ăźäœ“ç©ăŻ 22.4 L22.4 \mathrm{~L}.

10.4: 断熱過皋

  1. 断熱過皋: éŸłé€Ÿă«æŻ”ăčど遅く, 熱たć‡șć…„ă‚ŠăŒăȘい. pVÎł=p V^\gamma= const. (TVγ−1=\left(T V^{\gamma-1}=\right. const. )).

10.5: Îł=Cp/Cv=(i+2)/i

  1. Îł=cp/cv=(i+2)/i\gamma=c_p / c_v=(i+2) / i.

10.6: Boltzmann 戆澃

  1. Boltzmann 戆澃 :

    ρ=ρ0e−Mgh/RT=ρ0e−U/kBT\rho=\rho_0 e^{-M g h / R T}=\rho_0 e^{-U / k_B T}

10.7: Maxwell 戆澃

  1. Maxwell ćˆ†ćžƒïŒˆv ăźé€Ÿă•ă‚’ă‚‚ă€ćˆ†ć­ăźæ•°ïŒ‰

    èšłè€…æłš

    䜍盞ç©ș間で v\boldsymbol{v} ず v+dv\boldsymbol{v}+\mathrm{d} \boldsymbol{v} ăźé–“ă«ă‚ă‚‹ćˆ†ć­ăźæ•°ăźćˆ†ćžƒ ă§ă‚ă‚ŠïŒŒv ăźé€Ÿă•ă‚’ă‚‚ă€ćˆ†ć­ăźæ•°ăźćˆ†ćžƒăšăŻç•°ăȘる] ∝e−mv2/2kBT\propto e^{-m \boldsymbol{v}^2 / 2 k_B T}

10.8: ć€§æ°—ćœ§

  1. ć€§æ°—ćœ§ : Δpâ‰Șp\Delta p \ll p ăȘらば Δp=ρgΔh\Delta p=\rho g \Delta h.

10.9: ć…ŹćŒ

  1. p=13mnv2‟=nkBT(np=\frac{1}{3} m n \overline{v^2}=n k_B T(n ăŻæ•°ćŻ†ćșŠ ),v2‟‟=), \sqrt{\overline{\overline{v^2}}}= 3kBT/m,Îœ=vnS\sqrt{3 k_B T / m}, \nu=v n S.

10.10: Carnot ă‚”ă‚€ă‚Żăƒ«

  1. Carnot ă‚”ă‚€ă‚Żăƒ« : 断熱過皋 2 ă€ăšç­‰æž©éŽçš‹ 2 ぀. S−TS-T ćș§æš™ă‚’ç”šă„ă‚‹ă“ăšă«ă‚ˆă‚Š η=(T1−T2)/T1\eta=\left(T_1-T_2\right) / T_1 ă‚’ćŸ—ă‚‹.

10.11: ăƒ’ăƒŒăƒˆăƒăƒłăƒ—

  1. ăƒ’ăƒŒăƒˆăƒăƒłăƒ—: Carnot ă‚”ă‚€ă‚Żăƒ«ăźé€†. η=T1T1−T2\eta=\frac{T_1}{T_1-T_2}.

10.12: ă‚šăƒłăƒˆăƒ­ăƒ”ăƒŒ

  1. ă‚šăƒłăƒˆăƒ­ăƒ”ăƒŒ :dS=dQ/T: \mathrm{d} S=\mathrm{d} Q / T.

10.13: ç†±ćŠ›ć­ŠçŹŹäž€æł•ć‰‡

  1. ç†±ćŠ›ć­ŠçŹŹäž€æł•ć‰‡ : dâ€ČU=dâ€ČA+dâ€ČQ\mathrm{d}^{\prime} U=\mathrm{d}^{\prime} A+\mathrm{d}^{\prime} Q

10.14: 熱抛歊珏äșŒæł•ć‰‡

  1. 熱抛歊珏äșŒæł•ć‰‡ : ΔS≄0\Delta S \geq 0 (ăŸăŸ ηreal ≀ηCarnot )\left.\eta_{\text {real }} \leq \eta_{\text {Carnot }}\right).

10.15: æ°—äœ“ăźă™ă‚‹ä»•äș‹

  1. æ°—äœ“ăźă™ă‚‹ä»•äș‹ïŒˆăƒă‚€ăƒłăƒˆ 10 ă‚‚ć‚ç…§ïŒ‰:

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

10.16: Dalton ăźæł•ć‰‡

  1. Dalton ăźæł•ć‰‡: p=p= ∑pi\sum p_i

    èšłè€…æłš

    ç†æƒłæ°—äœ“ăźăżæˆç«‹

10.17: æČžéš°

  1. æČžéš°: éŁœć’Œè’žæ°—ăźćœ§ćŠ› pv=p0.2p_v=p_0 .2 æ¶Čぼ界靱では pv1+pv2=p0p_{v 1}+p_{v 2}=p_0.

10.18: 熱攁

  1. 熱攁: P=kSΔT/lP=k S \Delta T / l ( kk ăŻç†±äŒć°ŽçŽ‡). ç›Žæ”ć›žè·Żă«äŒŒăŠ いる (P↔I,ΔT↔V,k↔1/ρ)(P \leftrightarrow I, \Delta T \leftrightarrow V, k \leftrightarrow 1 / \rho).

10.19: 熱ćźč量

  1. 熱ćźč量 : Q=∫c(T)dTQ=\int c(T) \mathrm{d} T. ć›șäœ“ă§ăŻäœŽæž©ă§ c∝T3c \propto T^3, é«˜æž©ă§ c=3NkBc=3 N k_B Dulong-Petit ăźæł•ć‰‡. ここで NN ăŻç”æ™¶äž­ăźćŽŸć­æ•°ïŒ‰

10.20: èĄšéąćŒ”ćŠ›

  1. èĄšéąćŒ”ćŠ› :

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

10.21: Stefan-Boltzmann ăźæł•ć‰‡ (灰è‰Č䜓)

  1. Stefan-Boltzmann ăźæł•ć‰‡ (灰è‰Č䜓) : P=ΔσAT4P=\varepsilon \sigma A T^4.

10.22: Wien ăźć€‰äœć‰‡

  1. Wien ăźć€‰äœć‰‡: Îœmax⁥=AkBT/h(A≈\nu_{\max }=A k_B T / h(A \approx 2.8), λmax⁥=hc/Aâ€ČkBT(Aâ€Č≈5)\lambda_{\max }=h c / A^{\prime} k_B T\left(A^{\prime} \approx 5\right).
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/11.html b/academic/physics/ipho-formulas-jpn/11.html new file mode 100644 index 00000000..5f6e9484 --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/11.html @@ -0,0 +1,49 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 11 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 11

11: 量歐抛歩

11.1:p=hk

  1. p=ℏk(∣p∣=h/λ),E=ℏω=hÎœ\boldsymbol{p}=\hbar \boldsymbol{k}(|\boldsymbol{p}|=h / \lambda), E=\hbar \omega=h \nu.

11.2: ćčČ枉

  1. ćčČ枉 : æłąć‹•ć…‰ć­Šăźă‚ˆă†ă«.

11.3: 䞍çąșćźšæ€§

  1. 䞍çąșćźšæ€§ïŒˆæ•°ć­Šăźćźšç†ïŒ‰:

    ΔpΔx≄ℏ2,ΔEΔt≄ℏ2,ΔωΔt≄12\Delta p \Delta x \geq \frac{\hbar}{2}, \Delta E \Delta t \geq \frac{\hbar}{2}, \Delta \omega \Delta t \geq \frac{1}{2}

    æ»‘ă‚‰ă‹ă§ăȘă„ć Žćˆăźćźšæ€§çš„ăȘæŽšćźšă«ăŻ hh たæ–čăŒé©ă™ă‚‹ (ΔpΔx≈h(\Delta p \Delta x \approx h ăȘど )).

11.4: ă‚čăƒšă‚Żăƒˆăƒ«

  1. ă‚čăƒšă‚Żăƒˆăƒ« : hÎœ=En−Emh \nu=E_n-E_m. ă‚čăƒšă‚Żăƒˆăƒ«ç·šăźćč…は毿 ć‘œă«é–ąäż‚ă—, Γτ≈ℏ\Gamma \tau \approx \hbar.

11.5: æŒŻć‹•ć­

  1. æŒŻć‹•ć­ïŒˆäŸ‹ăˆă°ćˆ†ć­ïŒ‰ăźă‚šăƒăƒ«ă‚źăƒŒæș–䜍ć›șæœ‰æŒŻć‹•æ•° Îœ0):En=(n+12)hÎœ0\left.\nu_0\right): E_n=\left(n+\frac{1}{2}\right) h \nu_0. ć€šæ•°ăźć›șæœ‰æŒŻć‹•æ•°ăźć Žćˆ, E=∑hniÎœiE=\sum h n_i \nu_i.

11.6: ăƒˆăƒłăƒăƒ«ćŠč果

  1. ăƒˆăƒłăƒăƒ«ćŠč果: ćč… ll ぼ障棁 Γ\Gamma は, Γτ≈ℏ(τ=\Gamma \tau \approx \hbar(\tau= l/Γ/m)l / \sqrt{\Gamma / m}) であればćźčæ˜“ă«é€éŽă™ă‚‹.

11.7: Bohr ăƒąăƒ‡ăƒ«

  1. Bohr ăƒąăƒ‡ăƒ« : En∝−1/n2E_n \propto-1 / n^2. (ć€ć…žçš„ă«èšˆçź—ă•ă‚Œă‚‹) ć††è»Œé“ă§ăŻ, è»Œé“ăźé•·ă•ăŒæłąé•· λ=h/mv\lambda=h / m v ăźæ•Žæ•°ć€.

11.8: Compton ćŠč果

  1. Compton ćŠč果: ć…‰ć­ăŒé›»ć­ă‹ă‚‰æ•Łäč±ă•ă‚Œă‚‹ăš, 慉歐ぼ Δλ=λC(1−cos⁥Ξ)\Delta \lambda=\lambda_C(1-\cos \theta)

11.9: 慉電ćŠč果

  1. 慉電ćŠč果: W+mvmax⁥2/2=hÎœW+m v_{\max }^2 / 2=h \nu ( WW は仕äș‹é–ąæ•° )). I−VI-V ă‚°ăƒ©ăƒ•ïŒšć…‰é›»æ”ăŻé˜»æ­ąé›»ćœ§ V=−(hΜ−W)/eV=-(h \nu-W) / e ă§ć§‹ăŸă‚Š, æ­Łæ–čć‘ă«é›»ćœ§ăŒć€§ăăăȘă‚‹ăšç·©ć’Œă™ă‚‹.

11.10: Stefan-Boltzmann ăźæł•ć‰‡

  1. Stefan-Boltzmann ăźæł•ć‰‡ : P=σAT4P=\sigma A T^4
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/12.html b/academic/physics/ipho-formulas-jpn/12.html new file mode 100644 index 00000000..6feb0b80 --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/12.html @@ -0,0 +1,39 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 12 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 12

12: Kepler ăźæł•ć‰‡

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 ăźçŹŹäž€æł•ć‰‡

  1. Kepler ăźçŹŹäž€æł•ć‰‡ (2 èłȘç‚čぼ重抛盾äș’䜜甚)ïŒšăă‚Œăž ă‚Œăźè»Œé“ăŻïŒŒçł»ăźèłȘé‡äž­ćżƒă«ç„Šç‚čă‚’æŒă€æ„•ć††ïŒŒćŒæ›Č線, æ”Ÿç‰©ç·šă«ăȘる. これは Runge-Lenz ăƒ™ă‚Żăƒˆăƒ«ă‹ă‚‰ćŸ—ă‚‰ れる (ăƒă‚€ăƒłăƒˆ 9).

12.3: Kepler た珏äșŒæł•ć‰‡

  1. Kepler た珏äșŒæł•ć‰‡ïŒˆè§’é‹ć‹•é‡ăźäżć­˜ïŒ‰: 侭濃抛が惍く 栎にあるèłȘç‚čă«ă€ă„ăŠïŒŒăăźäœçœźăƒ™ă‚Żăƒˆăƒ«ăŻć˜äœæ™‚é–“ ă«äž€ćźšăźéąç©ă‚’æă.

12.4: Kepler ăźçŹŹäž‰æł•ć‰‡

  1. Kepler ăźçŹŹäž‰æł•ć‰‡ :r−2: r^{-2} ă«æŻ”äŸ‹ă™ă‚‹ćŠ›ăŒćƒăć Žă§æ„•ć†† è»Œé“ă‚’æăè€‡æ•°ăźèłȘç‚čに぀いお, ć‘šæœŸăŻé•·ćŠćŸ„ăź 32\frac{3}{2} äč— ă«æŻ”äŸ‹ă™ă‚‹ :

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

12.5: æ„•ć††è»Œé“

  1. é‡ćŠ›ć Žäž­ă§æ„•ć††è»Œé“ă‚’æăèłȘç‚čăźć…šă‚šăƒăƒ«ă‚źăƒŒ (K+U)(K+U) :

    E=−GMm/2aE=-G M m / 2 a

12.6: æ„•ć††çŽ‡

  1. æ„•ć††çŽ‡ăŒ Δ=d/aâ‰Ș1\varepsilon=d / a \ll 1 た栎搈, è»Œé“ăŻç„Šç‚čをずらし ăŸć††ćœąă‚’ă—ăŠă„ă‚‹ăšè€ƒăˆă‚‰ă‚Œă‚‹.

12.7: æ„•ć††ăźæ€§èłȘ

  1. æ„•ć††ăźæ€§èłȘ :l1+l2=2al1: l_1+l_2=2 a  l_1 ず l2l_2 は焩ç‚čăŸă§ăźè· 雱). α1=α2\alpha_1=\alpha_2 (侀æ–čぼ焩ç‚čからć‡șăŸć…‰ăŻä»–æ–čぼ焩ç‚čに 揍氄する). S=πabS=\pi a b.

12.8: 憆ぼ侭濃

  1. ć††ăšăăźć††ăźäž­ćżƒă«ç„Šç‚čă‚’ă‚‚ă€æ„•ć††ăŻé•·è»žăźéƒšćˆ†ă§ăź ăżæŽ„ă™ă‚‹.

12.9: nge-Lenz ăƒ™ă‚Żăƒˆăƒ« supplemental

  1. Runge-Lenz ăƒ™ă‚Żăƒˆăƒ«ïŒˆæ„•ć††çŽ‡ăƒ™ă‚Żăƒˆăƒ«ïŒ‰[èšłè€…æłšïŒšă“ ăźăƒ™ă‚Żăƒˆăƒ«ăŻă‚€ă—ă‚é›ąćżƒçŽ‡ăšé–ąäż‚ă™ă‚‹.そこでここで ăŻé›ąćżƒçŽ‡ăƒ™ă‚Żăƒˆăƒ«ăšă—ăŠçŸ„ă‚‰ă‚Œă‚‹ăƒ™ă‚Żăƒˆăƒ«ă‚’ä»Łă‚ă‚Šă« èš˜ă™.これは焩ç‚čă‹ă‚‰èż‘æ—„ç‚čă«ć‘ă‹ă†ć‘ăă§ïŒŒć€§ăă• が雱濃率 ee ă«äž€è‡Žă™ă‚‹.]

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

+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/13.html b/academic/physics/ipho-formulas-jpn/13.html new file mode 100644 index 00000000..e3fde34c --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/13.html @@ -0,0 +1,99 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 13 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 13

13: ç›žćŻŸæ€§ç†è«–

13.1:Lorentz ć€‰æ›

  1. Lorentz ć€‰æ› (Minkowski ćčŸäœ•ć­Šăź 4 æŹĄć…ƒæ™‚ç©șぼ曞 è»ąïŒ‰(æ…Łæ€§çł»é–“ăźé€ŸćșŠăŒ V=Vex):ÎČ=V/c,Îł=\left.\boldsymbol{V}=V \boldsymbol{e}_x\right): \beta=V / c, \gamma=

    1/1−ÎČ2 べしど, ctâ€Č=Îł(ct−ÎČx),xâ€Č=Îł(x−ÎČct),yâ€Č=yEâ€Č/c=Îł(E/c−ÎČpx),pxâ€Č=Îł(px−ÎČE/c),pyâ€Č=py ここで, E=mc21−v2/c2=mc2+12mv2+⋯px=mvx1−v2/c2, etc. \begin{aligned} & 1 / \sqrt{1-\beta^2} \text { べしど, } \\ & \qquad c t^{\prime}=\gamma(c t-\beta x), x^{\prime}=\gamma(x-\beta c t), y^{\prime}=y \\ & E^{\prime} / c=\gamma\left(E / c-\beta p_x\right), p_x^{\prime}=\gamma\left(p_x-\beta E / c\right), p_y^{\prime}=p_y \\ & \text { ここで, } \\ & E=\frac{m c^2}{\sqrt{1-v^2 / c^2}}=m c^2+\frac{1}{2} m v^2+\cdots \\ & p_x=\frac{m v_x}{\sqrt{1-v^2 / c^2}}, \text { etc. } \end{aligned}

13.2: 4 ć…ƒăƒ™ă‚Żăƒˆăƒ«ăźé•·

  1. 4 ć…ƒăƒ™ă‚Żăƒˆăƒ«ăźé•·ă• (ă‚čă‚«ăƒ©ăƒŒé‡ă§ă‚ă‚Š Lorentz ć€‰æ› ă§äžć€‰ïŒ‰:

    s2=(ct)2−x2−y2−z2(mc)2=(E/c)2−px2−py2−pz2\begin{aligned} s^2 & =(c t)^2-x^2-y^2-z^2 \\ (m c)^2 & =(E / c)^2-p_x^2-p_y^2-p_z^2 \end{aligned}

13.3: 速ćșŠăźćŠ çź—

  1. 速ćșŠăźćŠ çź— :

    vx=vxâ€Č+V1+vxâ€ČV/c2,vy=vyâ€ČÎł(1+vxâ€ČV/c2)v_x=\frac{v_x^{\prime}+V}{1+v_x^{\prime} V / c^2}, v_y=\frac{v_y^{\prime}}{\gamma\left(1+v_x^{\prime} V / c^2\right)}

13.4: Doppler ćŠč果

  1. Doppler ćŠč果 :

    Îœ=Îł(1+ÎČcos⁥Ξ)Îœ0\nu=\gamma(1+\beta \cos \theta) \nu_0

13.5: Minkowski ç©ș間

  1. Minkowski ç©ș間は, æ™‚é–“ăŒè™šæ•°ïŒˆ (tict)(t i c t) であれば Euclid ç©șé–“ă«ă™ă‚‹ă“ăšăŒă§ăă‚‹. ć›žè»ąè§’ φ\varphi ă«ćŻŸă—ăŠ, tanâĄÏ†=v/ic\tan \varphi=v / i c ずăȘり, sinâĄÏ†,cosâĄÏ†\sin \varphi, \cos \varphi を tanâĄÏ†\tan \varphi ă§èĄšă—ăŠ Euclid ćčŸäœ•ć­Šăźć…ŹćŒă‚’適甚する (Lorentz ć€‰æ›).

13.6: 長さた瞟み

  1. 長さた瞟み : lâ€Č=l0/Îłl^{\prime}=l_0 / \gamma.

13.7: æ™‚é–“ăźé…ă‚Œ

  1. æ™‚é–“ăźé…ă‚Œ: tâ€Č=t0Îłt^{\prime}=t_0 \gamma.

13.8: ćŒæ™‚ćˆ»ăźç›žćŻŸæ€§

  1. ćŒæ™‚ćˆ»ăźç›žćŻŸæ€§ : Δt=−γvΔx/c2\Delta t=-\gamma v \Delta x / c^2.

13.9: F=dp/dt

  1. F=dp/dt(=ddt(γmv))(\boldsymbol{F}=\mathrm{d} \boldsymbol{p} / \mathrm{d} t\left(=\frac{\mathrm{d}}{\mathrm{d} t}(\gamma m \boldsymbol{v})\right)( ここでぼ γ=\gamma= 1/1−v2/c2)\left.1 / \sqrt{1-v^2 / c^2}\right)

13.10: è¶…ç›žćŻŸè«–çš„æ„”é™

  1. è¶…ç›žćŻŸè«–çš„æ„”é™ :v≈c,p≈mc,1−(v/c)2≈: v \approx c, p \approx m c, \sqrt{1-(v / c)^2} \approx 2(1−v/c)\sqrt{2(1-v / c)}

13.11: 電栎ず磁栎た Lorentz ć€‰æ› supplemental

  1. 電栎ず磁栎た Lorentz ć€‰æ› : E∄â€Č=E∄,B∄â€Č=B∄\boldsymbol{E}_{\|}^{\prime}=\boldsymbol{E}_{\|}, \boldsymbol{B}_{\|}^{\prime}=\boldsymbol{B}_{\|},

    E⊄â€Č/c=Îł(E⊄/c+v/c×B⊄),B⊄â€Č=Îł(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}

+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/2.html b/academic/physics/ipho-formulas-jpn/2.html new file mode 100644 index 00000000..2309fbc5 --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/2.html @@ -0,0 +1,39 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 2 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 2

2: äž€èˆŹçš„ăȘæŽšć„šäș‹

  1. ć…šăŠăźèšˆçź—ćŒăźæ­Łă—ă•ă‚’çąșă‹ă‚ă‚‹ïŒša) æŹĄć…ƒă‚’èȘżăčる. b) 簡捘でç‰č戄ăȘ栮搈をèȘżăčă‚‹ïŒˆ2 ă€ăźć€‰æ•°ăŒç­‰ă—ă„, 1 ă€ăźć€‰æ•°ăŒ 0 ăŸăŸăŻ ∞\infty ). c) è§Łăźćźšæ€§çš„ăȘæŒ™ć‹•ăźćŠ„ćœ“ æ€§ă‚’èȘżăƒ™ă‚‹. 2.ă‚‚ă—ć•éĄŒæ–‡äž­ă«é©šăăƒ™ăć¶ç„¶ăźäž€è‡ŽăŒă‚ă‚Œă°ïŒˆäŸ‹ăˆă° 2 ă€ăźă‚‚ăźăŒćŒă˜), è§Łç­”ăźé”ăŻăă“ă«ă‚ă‚‹ă‹ă‚‚ă—ă‚Œ ăȘい.
  2. ć•éĄŒæ–‡äž­ăźæŽšć„šäș‹é …ă‚’ă‚ˆăèȘ­ă‚€. äș›çŽ°ăȘéƒšćˆ†ă«é‡èŠăȘ æƒ…ć ±ăŒć«ăŸă‚ŒăŠă„ă‚‹ć ŽćˆăŒă‚ă‚‹ăźă§ïŒŒć•éĄŒæ–‡ăźæ–‡èš€ă« æłšæ„ă™ă‚‹. かăȘă‚Šæ™‚é–“ă‚’ă‹ă‘ăŠă‚‚ć•éĄŒăŒè§Łă‘ăȘい栮搈 は, 敏題をèȘ€è§Łă—ăŠă„ă‚‹ă‹ă‚‚ă—ă‚ŒăȘいぼで, もう侀ćșŠ ć•éĄŒæ–‡ă‚’èȘ­ă‚€.
  3. é•·ăăŠæ™‚é–“ăźă‹ă‹ă‚‹èšˆçź—ăŻ, ç°Ąç•„ćŒ–ă—ăȘければăȘらăȘ い構めぼæ–čçš‹ćŒă‚’ć…šăŠæ›žăć‡șしたぼち, æœ€ćŸŒïŒˆä»–ăźć…š ăŠăŒç”‚ă‚ăŁăŸăšă) ăŸă§ć…ˆé€ă‚Šă™ă‚‹.
  4. ç”¶æœ›çš„ă«é›Łă—ă„ăšæ€ă‚ă‚Œă‚‹ć•éĄŒă§ă‚‚ïŒŒăŸă„ăŠă„éžćžžă« ă‚·ăƒłăƒ—ăƒ«ăȘè§Łæł•ăŒă‚ă‚‹.ă‚ȘăƒȘăƒłăƒ”ăƒƒă‚Żăźć•éĄŒă«é™ăŁăŠ èš€ăˆă°ïŒŒç”¶ćŻŸă«è§Łă‘ă‚‹.
  5. 漟鹓では, a) æžŹćźšă™ă‚‹ă»ă©ăźæ™‚ć•ăŒç„Ąă„ăšă—ăŠă‚‚, 漟 éš“èšˆç”»ăźæŠ‚ç•„ă‚’æ›žăïŒŒb) ç”æžœăźæ­Łçąșă•ă‚’é«˜ă‚ă‚‹æ–čæł•ă‚’ è€ƒăˆă‚‹ïŒŒc) æžŹćźšă—ăŸć€Œă‚’ć…šăŠïŒˆèĄšăšă—ăŠïŒ‰æ›žăć‡șす.
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/3.html b/academic/physics/ipho-formulas-jpn/3.html new file mode 100644 index 00000000..9e00de97 --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/3.html @@ -0,0 +1,39 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 3 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 3

3: 運拕歩

3.1: èłȘç‚č

  1. èłȘç‚čăŸăŸăŻć‰›äœ“ăźäžŠé€Čé‹ć‹•ăźć ŽćˆïŒˆç©ćˆ† → ă‚°ăƒ©ăƒ•ăźäž‹ ăźéąç©ïŒ‰ïŒš

    v=dxdt,x=∫vdt(x=∫vx dt ăȘ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 { ăȘ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 ăŒćźšæ•°ăȘらば, ă“ă‚Œă‚‰ăźç©ćˆ†ăŻç°Ąć˜ă«æ±‚ă‚ă‚‹ă“ べができど, äŸ‹ăˆă°

    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: ć›žè»ąé‹ć‹•

  1. ć›žè»ąé‹ć‹•ăŻ, 䞊é€Čé‹ć‹•ăšäŒŒăŠă„ăŠïŒš

    ω=dφ/dt,Δ=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: æ›Č線運拕

  1. æ›Čç·šé‹ć‹•ăŻïŒŒăƒă‚€ăƒłăƒˆ 1 ăšćŒă˜ă ăŒïŒŒăƒ™ă‚Żăƒˆăƒ«ăŻç·šé€Ÿ ćșŠïŒŒćŠ é€ŸćșŠïŒŒç”Œè·Żé•·ă«çœźăæ›ăˆă‚‹.

3.4: ć‰›äœ“ăźé‹ć‹•

  1. ć‰›äœ“ăźé‹ć‹•:
    • vAcos⁥α=vBcos⁥ÎČv_A \cos \alpha=v_B \cos \beta ここで, vA\boldsymbol{v}_A ず vB\boldsymbol{v}_B ăŻć‰›äœ“äžŠăźç‚č AA ず BB ぼ速ćșŠ, α\alpha ず ÎČ\beta は vA\boldsymbol{v}_A ず vB\boldsymbol{v}_B ăŒç›Žç·š ABA B ずăȘă™è§’.
    • çžŹé–“ć›žè»ąäž­ćżƒ (#èłȘç‚čăźè»Œé“ たæ›ČçŽ‡äž­ćżƒïŒ‰ăŻ, a\boldsymbol{a} ず b\boldsymbol{b} ă«äž‹ă‚ă—ăŸćž‚ç·šăźäș€ç‚č. 揈は もし vA,vB⊄AB\boldsymbol{v}_A, \boldsymbol{v}_B \perp A B ăȘらば, vA\boldsymbol{v}_A ず vB\boldsymbol{v}_B ăźć…ˆç«Żă‚’ç”ă¶ 盎線ず ABA B たäș€ç‚č.

3.5: éžæ…Łæ€§çł»

  1. éžæ…Łæ€§çł»ïŒš

    v2=v0+v1,a2=a0+a1+ω2R+aCor ここで, aCor⊄v1. もし v1=0 ăȘ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 { ăȘら } \boldsymbol{a}_{C o r}=0 . \end{array}

3.6: ćŒŸé“ć•éĄŒ supplemental

  1. ćŒŸé“ć•éĄŒïŒšćˆ°é”ćŻèƒœăȘ範ć›Čは

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

    最適ăȘćŒŸé“ă§ăŻ, 戝速ćșŠăšç”‚é€ŸïŒˆèĄçȘæ™‚ăźé€ŸćșŠïŒ‰ăŒćž‚盎 にăȘる.

3.7: æœ€çŸ­ç”Œè·Ż

  1. æœ€çŸ­ç”Œè·Żă‚’æ±‚ă‚ă‚‹ă«ăŻïŒŒFermat ず Huygens ぼ掟理が äœżăˆă‚‹.

3.8: ăƒ™ă‚Żăƒˆăƒ«

  1. ăƒ™ă‚Żăƒˆăƒ«ïŒˆé€ŸćșŠïŒŒćŠ é€ŸćșŠïŒ‰ă‚’æ±‚ă‚ă‚‹ă«ăŻïŒŒăăźć‘ăăš ïŒˆć Žćˆă«ă‚ˆăŁăŠăŻć‚Ÿă„ăŸïŒ‰ă‚ă‚‹è»žăžăźć°„ćœ±ă‚’æ±‚ă‚ă‚Œă° 慅戆.
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 4

4: 抛歩

4.1: ć‰›äœ“ăźäșŒæŹĄć…ƒçš„ăȘćčłèĄĄ

  1. ć‰›äœ“ăźäșŒæŹĄć…ƒçš„ăȘćčłèĄĄ : 抛に぀いおた 2 ă€ăźćŒăšăƒˆăƒ« クに぀いおた 1 ă€ăźćŒ. 1 ïŒˆćˆăŻ 2 ïŒ‰ć€‹ăźćŠ›ă«ă€ă„ăŠăź ćŒăŻ 1ïŒˆćˆăŻ 2ïŒ‰ć€‹ăźăƒˆăƒ«ă‚Żă«ă€ă„ăŠăźćŒă§ä»Łç”šă§ă る. ăƒˆăƒ«ă‚Żăźæ–čăŒè‰Żă„ć ŽćˆăŒć€šăïŒŒćŽŸç‚čă‚’é©ćˆ‡ă«éžæŠž ă™ă‚‹ă“ăšă§ă€Œé€€ć±ˆăȘă€ćŠ›ă‚’æ¶ˆă™ă“ăšăŒă§ăă‚‹. もし 2 ç‚č ăźăżă«ćŠ›ăŒă‹ă‹ăŁăŠă„ă‚‹ăȘă‚‰ă°ïŒŒïŒˆæ­Łć‘łăźïŒ‰ćŠ›ăŒă‹ă‹ăŁ ăŠă„ă‚‹ç›Žç·šăŻäž€è‡Žă™ă‚‹. 3 ç‚čであれば, 3 ぀た盎線は 1 ç‚čでäș€ă‚ă‚‹.

4.2: ćž‚ç›ŽæŠ—ćŠ›

  1. ćž‚ç›ŽæŠ—ćŠ›ăšæ‘©æ“ŠćŠ›ăŻ 1 ă€ăźćŠ›ă«ćˆæˆă§ă, ćž‚ç›ŽæŠ—ćŠ›ă« ćŻŸă—ăŠ arctanâĄÎŒ\arctan \mu ăźè§’ćșŠă§æŽ„觊ç‚čă«ćŠ ă‚ă‚‹.

4.3: 䞊é€Čé‹ć‹•ăšć›žè»ąé‹ć‹•

  1. 䞊é€Čé‹ć‹•ăšć›žè»ąé‹ć‹•ă«ă€ă„ăŠăź Newton た珏äșŒæł•ć‰‡ïŒš

    F=ma,M=IΔ(M=r×F)\boldsymbol{F}=m \boldsymbol{a}, \boldsymbol{M}=I \boldsymbol{\varepsilon} \quad(\boldsymbol{M}=\boldsymbol{r} \times \boldsymbol{F})

    äșŒæŹĄć…ƒăźć Žćˆă«ăŻ MM ず Δ\varepsilon ăŻæœŹèłȘ的にă‚čă‚«ăƒ©ăƒŒă§, M=Fl=Ftr(lM=F l=F_t r(l は抛たうでた長さ ))

4.4: äž€èˆŹćŒ–ćș§æš™

  1. äž€èˆŹćŒ–ćș§æš™. çł»ăźçŠ¶æ…‹ăŒ 1 ă€ăźć€‰æ•° Ο\xi ăšăăźæ™‚é–“ćŸźćˆ† Ο˙\dot{\xi} ă§èĄšă•ă‚ŒïŒŒăƒăƒ†ăƒłă‚·ăƒŁăƒ«ă‚šăƒăƒ«ă‚źăƒŒăŒ U=U(Ο)U=U(\xi), é‹ć‹•ă‚šăƒăƒ«ă‚źăƒŒăŒ K=ΌΟ2/2K=\mu \xi^2 / 2 であるăȘらば, ΌΟš=\mu \ddot{\xi}= −dU(Ο)/dΟ-\mathrm{d} U(\xi) / \mathrm{d} \xi. (したがっど侩é€Č運拕では, 抛はポテン ă‚·ăƒŁăƒ«ă‚šăƒăƒ«ă‚źăƒŒăźćŸźćˆ†)

4.5: çł»èłȘç‚č

  1. çł»ăŒèłȘç‚č mim_i ă§æ§‹æˆă•ă‚ŒăŠă„ă‚‹ăšăïŒš

    rc=∑miri/∑mj,P=∑miviL=∑miri×vi,K=∑mivi2/2Iz=∑mi(xi2+yi2)=∫(x2+y2)dm\begin{aligned} & \boldsymbol{r}_c=\sum m_i \boldsymbol{r}_i / \sum m_j, \boldsymbol{P}=\sum m_i \boldsymbol{v}_i \\ & \boldsymbol{L}=\sum m_i \boldsymbol{r}_i \times \boldsymbol{v}_i, K=\sum m_i v_i^2 / 2 \\ & I_z=\sum m_i\left(x_i^2+y_i^2\right)=\int\left(x^2+y^2\right) \mathrm{d} m \\ & \end{aligned}

4.6: èłȘ量侭濃ぼ速ćșŠ

  1. èłȘ量侭濃ぼ速ćșŠăŒ vc\boldsymbol{v}_c であるようăȘçł» (æ·»ăˆć­— cc はèłȘ量 äž­ćżƒă«ă€ă„ăŠăźç‰©ç†é‡ă§ă‚ă‚‹ă“ăšă‚’ç€șă™ïŒ‰:

    L=Lc+MΣRc×vc,K=Kc+MΣvc2/2P=Pc+MΣvc.\begin{gathered} \boldsymbol{L}=\boldsymbol{L}_c+M_{\Sigma} \boldsymbol{R}_c \times \boldsymbol{v}_c, K=K_c+M_{\Sigma} v_c^2 / 2 \\ \boldsymbol{P}=\boldsymbol{P}_c+M_{\Sigma} \boldsymbol{v}_c . \end{gathered}

4.7: Steiner 漚理

  1. Steiner ăźćźšç†ïŒˆćčłèĄŒè»žăźćźšç†ïŒ‰ă‚‚ćŒă˜ă‚ˆă†ăȘćœąă§ はèłȘé‡äž­ćżƒăźć›žè»ąè»žă‹ă‚‰ăźè·é›ąïŒ‰:

    I=Ic+mb2I=I_c+m b^2

4.8: ăƒă‚€ăƒłăƒˆ 6

  1. ăƒă‚€ăƒłăƒˆ 6 た P\boldsymbol{P} ず L\boldsymbol{L} を甹いど, Newton た珏äșŒæł•ć‰‡ :

    FÎŁ=dP/dt,MÎŁ=dL/dt\boldsymbol{F}_{\Sigma}=\mathrm{d} \boldsymbol{P} / \mathrm{d} t, \boldsymbol{M}_{\Sigma}=\mathrm{d} \boldsymbol{L} / \mathrm{d} t

4.9: ăƒă‚€ăƒłăƒˆ 5

  1. ăƒă‚€ăƒłăƒˆ 5 ă«ă«ćŠ ăˆăŠïŒŒèłȘ量侭濃を通る zz è»žă«ćŻŸă™ă‚‹æ…Łæ€§ăƒąäž€ăƒĄăƒłăƒˆăŻ Iz0=I_{z 0}= ∑i,jmimj[(xi−xj)2+(yi−yj)2]/(2MÎŁ)\sum_{i, j} m_i m_j\left[\left(x_i-x_j\right)^2+\left(y_i-y_j\right)^2\right] /\left(2 M_{\Sigma}\right)

4.10: 掟ç‚čă«ćŻŸă™ă‚‹æ…Łæ€§

  1. 掟ç‚čă«ćŻŸă™ă‚‹æ…Łæ€§ăƒąäž€ăƒĄăƒłăƒˆ Ξ=∑miri2\theta=\sum m_i r_i^2 は, 2Ξ=Ix+Iy+Iz2 \theta=I_x+I_y+I_z を甹いるこべでäșŒæŹĄć…ƒç‰©äœ“ă‚„ç­‰ æ–čæ€§ăźă‚ă‚‹ç‰©äœ“ăź IzI_z ă‚’èšˆçź—ă™ă‚‹ăźă«æœ‰ç”š.

4.11: ç›žćœ“ć˜æŒŻć­ăźé•·

  1. ç›žćœ“ć˜æŒŻć­ăźé•·ă•ăŒ l~\tilde{l} ă§ă‚ă‚‹ç‰©ç†æŒŻć­ :

    ω2(l)=g/(l+Ic/ml)ω(l)=ω(l~−l)=g/l~,l~=l+Ic/ml\begin{aligned} & \omega^2(l)=g /\left(l+I_c / m l\right) \\ & \omega(l)=\omega(\tilde{l}-l)=\sqrt{g / \tilde{l}}, \quad \tilde{l}=l+I_c / m l \\ & \end{aligned}

4.12: æ…Łæ€§ăƒąăƒŒăƒĄăƒłăƒˆăźäż‚æ•°

  1. æ…Łæ€§ăƒąăƒŒăƒĄăƒłăƒˆăźäż‚æ•° : ć††æŸ± 12\frac{1}{2}, 球 25\frac{2}{5}, çƒæźŒ 23\frac{2}{3}, æŁ’ 112\frac{1}{12} ïŒˆç«Żă«ćŻŸă—ăŠăŻ 13\frac{1}{3} ), æ­Łæ–čćœą 16\frac{1}{6}.

4.13: ă‚ˆăäœżă‚ă‚Œă‚‹äżć­˜ć‰‡

  1. ă‚ˆăäœżă‚ă‚Œă‚‹äżć­˜ć‰‡ïŒšă‚šăƒăƒ«ă‚źăƒŒïŒˆćŒŸæ€§èĄçȘïŒŒæ‘©æ“ŠăȘ し), é‹ć‹•é‡ïŒˆæ­Łć‘łăźć€–ćŠ›ăȘし, 搄æ–čć‘ă«ă€ă„ăŠæˆç«‹), è§’é‹ć‹•é‡ïŒˆæ­Łć‘łăźć€–ăƒˆăƒ«ă‚ŻăȘし, äŸ‹ăˆă°, 怖抛たうでた é•·ă•ăŒ 0 (これが 2 揈は 3 ç‚čăźăŸă‚ă‚Šă«æˆă‚Šç«‹ăŠă°é‹ ć‹•é‡äżć­˜ă§ä»Łç”šă§ăă‚‹))

4.14: éžæ…Łæ€§çł»ă«ăŠă‘ă‚‹èŠ‹ă‹ă‘ăźćŠ›

  1. éžæ…Łæ€§çł»ă«ăŠă‘ă‚‹èŠ‹ă‹ă‘ăźćŠ› : æ…Łæ€§ćŠ› −ma-m a, 遠濃抛 mω2Rm \omega^2 \boldsymbol{R}, Coriolis 抛 2mv×Ω2 m \boldsymbol{v} \times \Omega (避けたæ–čがよい. 速 ćșŠă«ćž‚盎ăȘたで仕äș‹ăŻă—ăȘい).

4.15: ć‚Ÿă„ăŸćș§æš™

  1. ć‚Ÿă„ăŸćș§æš™ïŒšæ–œéąäžŠă§ăźé‹ć‹•ă«ă€ă„おは, æ–œéąă«ćčłèĄŒ べ枂目ăȘæ–čć‘ă«è»žă‚’ăšă‚‹ăźăŒă‚ˆă„ă€‚ă“ăźăšăé‡ćŠ›ćŠ é€Ÿ ćșŠăŻ xx æˆćˆ†ăš yy æˆćˆ†ă‚’ă‚‚ă€. è»žăŻæ–œäș€ă™ă‚‹ă“ずもある が, v=vxex+vyey\boldsymbol{v}=v_x \boldsymbol{e}_x+v_y \boldsymbol{e}_y ぼべき vxv_x は v\boldsymbol{v} た xx è»žăžăźć°„ ćœ±ă§ăŻăȘい.

4.16: 2 ă€ăźç‰©äœ“ăźèĄçȘ

  1. 2 ă€ăźç‰©äœ“ăźèĄçȘ : 保歘されるぼは, a) 慹運拕量, b) ć…šè§’é‹ć‹•é‡ïŒŒc) 侀æ–čăźç‰©äœ“ăźèĄçȘç‚čă«é–ąă™ă‚‹è§’é‹ć‹•é‡, d) ć…šă‚šăƒăƒ«ă‚źăƒŒïŒˆćŒŸæ€§èĄçȘăźć ŽćˆïŒŒ æ‘©æ“ŠăŒă‚ă‚‹ć Žćˆ は, æ‘©æ“ŠćŠ›ă«ćž‚ç›ŽăȘæ–čć‘ăźé‹ć‹•ă‚šăƒăƒ«ă‚źăƒŒăŒäżć­˜ă•ă‚Œă‚‹. e) èĄçȘäž­ă«æ»‘ă‚ŠăŒæ­ąăŸăŁăŸăȘă‚‰ă°ïŒŒæŽ„è§Šç‚čăźæœ€ç”‚ 速ćșŠăŻæŽ„è§ŠéąäžŠă«ă‚ă‚‹. f) æ»‘ă‚ŠăŒæ­ąăŸă‚‰ăȘかったăȘら ば, 侀æ–čăźç‰©äœ“ă‹ă‚‰ä»–æ–čă«äŒă‚ă‚‹é‹ć‹•é‡ăŻ, æŽ„è§Šéąăź æł•ç·šăš arctanâĄÎŒ\arctan \mu ăźè§’ćșŠă‚’ăȘす.

4.17: ć‰›äœ“ăźă™ăčどぼ運拕

  1. ć‰›äœ“ăźă™ăčどぼ運拕は (ç‰©äœ“ăźć„ç‚čぼ速ćșŠă‚’èŠ‹ă‚‹ăš) 瞬 é–“ć›žè»ąäž­ćżƒ CC ăŸă‚ă‚Šăźć›žè»ąăšă—ăŠèĄšă›ă‚‹. ç‰©äœ“äžŠăźç‚č PP た CC ă‹ă‚‰ăźè·é›ąăŻ PP ăźè»Œè·Ąăźæ›ČçŽ‡ćŠćŸ„ăšăŻç•°ăȘる ă“ăšă«æłšæ„ă›ă‚ˆ.

4.18: çŽăźćŒ”ćŠ›

  1. çŽăźćŒ”ćŠ›ïŒšé‡ă•ăźă‚ă‚‹ćŠă‚ŠçŽă§ăŻ, ćŒ”ćŠ›ăźæ°Žćčłæˆćˆ†ăŻ äž€ćźšă§ćž‚ç›Žæˆćˆ†ăŻäž‹ă«ă‚ă‚‹çŽăźé‡ă•ă«ă‚ˆă‚Šć€‰ă‚ă‚‹. 滑 らかăȘéąăźäžŠăźçŽă«ă‚ˆă‚‹ïŒˆć˜äœé•·ă•ă‚ăŸă‚ŠăźïŒ‰ćŠ›ăŻïŒŒă たæ›ČçŽ‡ćŠćŸ„ăšćŒ”ćŠ›ă§æ±șăŸă‚Š, N=T/RN=T / R. äŒŒăŸć Žćˆăš しど, èĄšéąćŒ”ćŠ›ă«ă‚ˆă‚‹ćœ§ćŠ›ăŻ p=2σ/Rp=2 \sigma / R. 氎ć‡șには盎 ćŸ„ă«æȿった朧抛をèȘżăƒ™ă‚‹.

4.19: æ¶Čäœ“ăźèĄšéą

  1. æ¶Čäœ“ăźèĄšéąăŻïŒˆèĄšéąćŒ”ćŠ›ă‚’ç„ĄèŠ–ă™ă‚Œă°ïŒ‰ç­‰ăƒăƒ†ăƒłă‚·ăƒŁ ăƒ«éąă«ăȘる. éžćœ§çžźæ€§æ”äœ“ă§ăŻ, ww ă‚’ăƒăƒ†ăƒłă‚·ăƒŁăƒ«ă‚š ăƒăƒ«ă‚źăƒŒăźäœ“ç©ćŻ†ćșŠăšă—お, p=P0−wp=P_0-w.

4.20: éžćœ§çžźæ€§æ”äœ“ă«ćŻŸă™ă‚‹ Bernoulli ăźæł•ć‰‡

  1. éžćœ§çžźæ€§æ”äœ“ă«ćŻŸă™ă‚‹ Bernoulli ăźæł•ć‰‡ïŒš

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

    䞀様ăȘ重抛栮では ϕ=gh\phi=g h. æŻ”ç†±ăŒ cp[ J/kg]c_p[\mathrm{~J} / \mathrm{kg}] ă§ă‚ă‚‹æ°— äœ“ă§ăŻ,

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

4.21: 盎線的ăȘ攁線 supplemental

  1. 盎線的ăȘæ”ç·šă«æČŸă†é‹ć‹•é‡ăźé€Łç¶šæ€§ : p+ρv2=p+\rho v^2= const.

4.22: æ–­ç†±äžć€‰é‡ supplemental

  1. æ–­ç†±äžć€‰é‡ : æŒŻć‹•ă™ă‚‹çł»ăź 1 ć‘šæœŸăźé–“ăźăƒ‘ăƒ©ăƒĄăƒŒă‚żăź ç›žćŻŸçš„ăȘć€‰ćŒ–ăŒć°ă•ă‘ă‚Œă°ïŒŒäœç›žç©ș間 x−px-p ćș§æš™ă§èĄšă• ă‚Œă‚‹ïŒ‰äžŠă«æ›žă‹ă‚Œă‚‹ăƒ«ăƒŒăƒ—ăźéąç©ăŻéžćžžă«é«˜ă„çČŸćșŠă§ 保歘される.

4.23: ćź‰ćźšæ€§

  1. ćź‰ćźšæ€§ă‚’èȘżăƒ™ă‚‹ă«ăŻ, a) ăƒăƒ†ăƒłă‚·ăƒŁăƒ«ă‚šăƒăƒ«ă‚źăƒŒæœ€ć° ăźćŽŸç†ïŒŒćˆăŻ b) ä»źæƒłä»•äș‹ăźćŽŸç†ă‚’甚いる.

4.24: ç©șé–“çš„ă«æœ‰é™ăȘé‹ć‹•ă«ćŻŸă™ă‚‹ Virial 漚理 supplemental

  1. ç©șé–“çš„ă«æœ‰é™ăȘé‹ć‹•ă«ćŻŸă™ă‚‹ Virial ćźšç†ïŒša) もし F∝∣r∣F \propto|\boldsymbol{r}| ăȘらば ⟹K⟩=⟹U⟩\langle K\rangle=\langle U\rangle (時間ćčłć‡). b) もし F∝∣r∣−2F \propto|\boldsymbol{r}|^{-2} ăȘらば 2⟹K⟩=−⟹U⟩2\langle K\rangle=-\langle U\rangle.

4.25: Tsiolkovsky ć…ŹćŒ

  1. Tsiolkovsky ăźć…ŹćŒïŒˆăƒ­ă‚±ăƒƒăƒˆïŒ‰: Δv=uln⁥Mm\Delta v=u \ln \frac{M}{m}
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 5

5. æŒŻć‹•ăšæłą

5.1: æž›èĄ°æŒŻć‹•

  1. æž›èĄ°æŒŻć‹•ïŒš

    xš+2Îłx˙+ω02x=0(Îł<ω)\ddot{x}+2 \gamma \dot{x}+\omega_0^2 x=0(\gamma<\omega)

    こぼæ–čçš‹ćŒăźè§ŁăŻ ((Section 1: #3)[1#_1-3-ćźšæ•°äż‚æ•°ç·šćœąćŸźćˆ†æ–čçš‹ćŒ] 揂照) :

    x=x0e−γtsin⁥(tω02−γ2−φ0)x=x_0 e^{-\gamma t} \sin \left(t \sqrt{\omega_0^2-\gamma^2}-\varphi_0\right)

5.2: é€ŁæˆæŒŻć‹•ăźćŒ

  1. é€ŁæˆæŒŻć‹•ăźćŒ : xši=∑jaijxj\ddot{x}_i=\sum_j a_{i j} x_j

5.3: é€ŁæˆæŒŻć‹•ăźçł»

  1. NN ć€‹ăźé€ŁæˆæŒŻć‹•ăźçł»ăŻ, すăčăŠăźæŒŻć‹•ć­ăŒćŒă˜æŒŻć‹•æ•° ωi\omega_i で xj=xj0sin⁥(ωit+φij)x_j=x_{j 0} \sin \left(\omega_i t+\varphi_{i j}\right) ăźă‚ˆă†ă«æŒŻć‹•ă™ă‚‹ăšă„ うć›șæœ‰ăƒąăƒŒăƒ‰ă‚’ NN ć€‹æŒă€. ć›șæœ‰æŒŻć‹•æ•° ωiもN\omega_i も N ć€‹æŒ ぀ (äž€è‡Žă™ă‚‹ă‹ă‚‚ă—ă‚ŒăȘい, ωi=ωj\omega_i=\omega_j ). äž€èˆŹè§Ł (2N(2 N ć€‹ăźç©ćˆ†ćźšæ•° Xi,ϕiX_i, \phi_i ă‚’æŒă€) は慹どぼć›șæœ‰æŒŻć‹•ăźé‡ă­ 搈わせ :

    xj=∑iXixj0sin⁥(ωit+φij+ϕi)x_j=\sum_i X_i x_{j 0} \sin \left(\omega_i t+\varphi_{i j}+\phi_i\right)

5.4: äž€èˆŹćŒ–ćș§æš™

  1. äž€èˆŹćŒ–ćș§æš™ Ο\xi ((Section 4: #4)[4#_4-4-äž€èˆŹćŒ–ćș§æš™] 揂照) ă§èĄšă•ă‚Œ K=ΌΟ˙2/2K=\mu \dot{\xi}^2 / 2 である系は, Ο=0\xi=0 たç‚čでćčłèĄĄ. 氏さăȘæŒŻć‹•ă«ă€ いど U(Ο)≈ÎșΟ2/2U(\xi) \approx \kappa \xi^2 / 2 (ここで Îș=Uâ€Čâ€Č(0))\left.\kappa=U^{\prime \prime}(0)\right) であり ω2=Îș/ÎŒ\omega^2=\kappa / \mu.

5.5: æłąăźäœç›ž

  1. x,tx, t ă§ăźæłąăźäœç›žăŻ φ=kx−ωt+φ0\varphi=k x-\omega t+\varphi_0 で, k=2π/λk=2 \pi / \lambda ăŻæłąæ•°. x,tx, t ă§ăźć€ŒăŻ a0cosâĄÏ†=Re⁥a0eiφa_0 \cos \varphi=\operatorname{Re} a_0 e^{i \varphi}. 䜍盞速 ćșŠăŻ vf=Μλ=ω/kv_f=\nu \lambda=\omega / k ă§ïŒŒ 矀速ćșŠăŻ vg=dω/dkv_g=\mathrm{d} \omega / \mathrm{d} k.

5.6: ç·šćœąæłą

  1. ç·šćœąæłąïŒˆé›»çŁæłą, ć°æŒŻćč…ăźéŸłæłąă‚„æ°ŽéąæłąïŒ‰ăźć Žćˆ, どん ăȘăƒ‘ăƒ«ă‚čæłąă‚‚æ­ŁćŒŠæłąăźé‡ă­ćˆă‚ă›ăšă—ăŠèĄšă›ă‚‹. 漚澾 æłąăŻ 2 ă€ăźé€†ć‘ăă«é€Čă‚€ćŒă˜æłąăźćˆæˆ :

    ei(kx−ωt)+ei(−kx−ωt)=2e−iωtcos⁥kte^{i(k x-\omega t)}+e^{i(-k x-\omega t)}=2 e^{-i \omega t} \cos k t

5.7: æ°—äœ“äž­ăźéŸłé€Ÿ

  1. æ°—äœ“äž­ăźéŸłé€Ÿ :

    cs=(∂p/∂ρ)断熱 =Îłp/ρ=Îłv2‟/3c_s=\sqrt{(\partial p / \partial \rho)_{\text {断熱 }}}=\sqrt{\gamma p / \rho}=\sqrt{\gamma \overline{v^2} / 3}

5.8: ćŒŸæ€§äœ“äž­ăźéŸłé€Ÿ

  1. ćŒŸæ€§äœ“äž­ăźéŸłé€ŸăŻ cs=E/ρc_s=\sqrt{E / \rho}.

5.9: æ”…æ°Žæłą

  1. æ”…æ°Žæłą (hâ‰Șλ)(h \ll \lambda) ぼ速さ: v=ghv=\sqrt{g h}. ćŒŠăźć ŽćˆïŒš v=T/ρlinv=\sqrt{T / \rho_{l i n}}.

5.10: Doppler ćŠč果

  1. Doppler ćŠč果 : Îœ=Îœ01+v∄/cs1−u∄/cs\nu=\nu_0 \frac{1+v_{\|} / c_s}{1-u_{\|} / c_s}.

5.11: Huygens ぼ掟理

  1. Huygens ぼ掟理 : æłąéąăŻæź”éšŽçš„ă«æ§‹æˆă•ă‚Œă‚‹. 過掻 ăźæłąéąăźă™ăčおたç‚čă«ä»źæƒłçš„ăȘæłąæșă‚’çœźă. ç”æžœăŻè· 雱 Δx=csΔt\Delta x=c_s \Delta t でćŒș戇られたæ›Čç·šïŒˆă“ă“ă§ Δt\Delta t ăŻæ™‚é–“ 間隔 csc_s は侎えられたç‚čぼ速ćșŠ). æłąăŻæłąéąă«ćž‚ç›Žă« é€Čむ.
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/6.html b/academic/physics/ipho-formulas-jpn/6.html new file mode 100644 index 00000000..1705612b --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/6.html @@ -0,0 +1,39 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 6 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 6

6: ćčŸäœ•ć…‰ć­ŠïŒŒæžŹć…‰

6.1: Fermat 掟理

  1. Fermat ぼ掟理 : ç‚č AA から BB ăžăźæłąăźç”Œè·ŻăŻæłąăźç§»ć‹• æ™‚é–“ăŒæœ€ă‚‚çŸ­ă„ă‚‚ăź.

6.2: Snell æł•ć‰‡

  1. Snell ăźæł•ć‰‡ :

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

6.3:

  1. ć±ˆæŠ˜çŽ‡ăŒé€Łç¶šçš„ă«ć€‰ćŒ–ă™ă‚‹ăȘă‚‰ă°ïŒŒćȘ’èłȘă‚’ć±ˆæŠ˜çŽ‡ăŒ nn ă§äž€ćźšăźă„ăă€ă‹ăźä»źæƒłçš„ăȘć±€ă«ćˆ†ă‘ăŠ Snell た æł•ć‰‡ă‚’é©ç”šă™ă‚‹. ć…‰ç·šăŻć±ˆæŠ˜çŽ‡äž€ćźšăźć±€ă«æȿっおé€Čむ こべもでき,ă‚‚ă—ć…šćć°„ăźæĄä»¶ă‚’ă‚ăšă‹ă«æș€ăŸă›ă°, nâ€Č=n/r(rn^{\prime}=n / r \quad(r はæ›ČçŽ‡ćŠćŸ„ ))

6.4:

  1. ć±ˆæŠ˜çŽ‡ăŒ z\mathrm{z} ćș§æš™ă«ăźăżäŸć­˜ă™ă‚‹ăȘらば, 慉歐ぼ運拕量 px,pyp_x, p_y ăšă‚šăƒăƒ«ă‚źăƒŒăŻäżć­˜ă•ă‚Œă‚‹:

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

6.5:è–„ă„ăƒŹăƒłă‚șăźćŒ

  1. è–„ă„ăƒŹăƒłă‚șăźćŒïŒˆçŹŠć·ă«æłšæ„ă™ă‚‹ïŒ‰ïŒš

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

6.6: Newton ăźćŒ

  1. Newton ăźćŒ : ç‰©äœ“ćŽç„Šç‚čă‹ă‚‰ç‰©äœ“ăŸă§ăźè·é›ąă‚’ x1x_1, 惏恮焩ç‚čă‹ă‚‰ćƒăŸă§ăźè·é›ąă‚’ x2x_2 べするべ, x1x2=f2x_1 x_2=f^2

6.7: ćƒăźäœçœźă‚’æ±‚ă‚ă‚‹èŠ–ć·źæł•

  1. ćƒăźäœçœźă‚’æ±‚ă‚ă‚‹èŠ–ć·źæł• : ç›źăźäœçœźăšćž‚ç›Žă«ć‹•ă‹ă—ăŸ ăšăă«ïŒŒé‰›ç­†ăźć…ˆăŒćƒă«ćŻŸă—ăŠăšă‚ŒăȘいようăȘäœçœźă‚’ æŽąă™.

6.8: ハンă‚șă‚’é€šă‚‹ć…‰ç·šăźç”Œè·ŻăźćčŸäœ•ć­Šçš„ăȘæăæ–č

  1. ハンă‚șă‚’é€šă‚‹ć…‰ç·šăźç”Œè·ŻăźćčŸäœ•ć­Šçš„ăȘæăæ–ča) ハン ă‚șăźäž­ćżƒă‚’é€šă‚‹ć…‰ç·šăŻć±ˆæŠ˜ă—ăȘい。b) ć…‰è»žă«ćčłèĄŒăȘ慉 線は焊ç‚čă‚’é€šă‚‹ïŒŒc) ć±ˆæŠ˜ćŸŒ, ćˆă‚ă«ćčłèĄŒă ăŁăŸć…‰ç·šă©ă†ă—は焊ç‚čéąïŒˆç„Šç‚čă‚’é€šă‚Šć…‰è»žă«ćž‚ç›ŽăȘćčłéąïŒ‰äžŠă§é›† ăŸă‚‹ïŒŽd) ćčłéąăźćƒăŻćčłéąă§ă‚ă‚ŠïŒŒă“ăź 2 ぀たćčłéąăŻăƒŹ ンă‚șたćčłéąäžŠă§äș€ă‚ă‚‹ïŒŽ

6.9: ć…‰æŸ

  1. ć…‰æŸ Ί\Phi [ć˜äœ: lumen (lm⁥)(\operatorname{lm})] は, ć…‰ăźă‚šăƒăƒ«ă‚źăƒŒ をç€șし, çœŒăźæ„ŸćșŠă«ćżœă˜ăŠé‡ăżä»˜ă‘ă•ă‚Œă‚‹. 慉ćșŠ [candela (cd)]ăŻïŒˆć…‰æșă‹ă‚‰ć‡șă‚‹ïŒ‰ç«‹äœ“è§’ă‚ăŸă‚Šăź ć…‰æŸă§, I=Ί/ΩI=\Phi / \Omega. 照ćșŠ [lux⁥(lx)][\operatorname{lux}(\mathrm{lx})] ăŻïŒˆéąă«ć…„ć°„ă™ă‚‹ïŒ‰ éąç©ă‚ăŸă‚Šăźć…‰æŸă§, E=Ί/SE=\Phi / S.

6.10: Gauss 漚理

  1. ć…‰æŸă«ă€ă„ăŠăź Gauss ぼ漚理 : 慉ćșŠ IiI_i たç‚č慉æșă‚’ć›Č む閉æ›Čéąă‚’é€šăŁăŠć€–ă«ć‡șă‚‹ć…‰æŸăŻ, Ί=4π∑Ii\Phi=4 \pi \sum I_i. 慉 æșăŒ 1 ă€ă§è·é›ąăŒ rr ぼべき E=I/r2E=I / r^2

6.11: 漟鹓ぼヒント

  1. ćźŸéš“ăźăƒ’ăƒłăƒˆïŒšçŽ™ă«ă€ă„ăŸæČčæ±Ąă‚ŒăŒć‘šć›ČăźçŽ™ăšćŒă˜æ˜Ž るさăȘă‚‰ă°ïŒŒăăźçŽ™ăŻäžĄéąă‹ă‚‰ćŒă˜ă‚ˆă†ă«ç…§ă‚‰ă•ă‚ŒăŠ いる.
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 7

7: æłąć‹•ć…‰ć­Š

7.1: Huygens ăźćŽŸç†ă«ćŸșă„ă„ăŸć›žæŠ˜

  1. Huygens ăźćŽŸç†ă«ćŸșă„ă„ăŸć›žæŠ˜ : éšœćźłç‰©ăŒæłąéąă‚’ćˆ‡æ–­ ă™ă‚‹ăšæłąéąăŻć°ă•ăȘæ–­ç‰‡ă«ćˆ†ć‰Čă•ă‚ŒïŒŒăă‚ŒăŒä»źæƒłçš„ăȘ ç‚čæłąæșăšăȘă‚ŠïŒŒèŠłæžŹç‚čă§ăźæłąăźæŒŻćč…ăŻă“ă‚Œă‚‰ăźæłąæșă‹ らぼ毄侎ぼ重ね搈わせべăȘる.

7.2: äșŒé‡ă‚čăƒȘット

  1. äșŒé‡ă‚čăƒȘăƒƒăƒˆïŒˆćč…は dâ‰Șa,λ)d \ll a, \lambda) ă«ă‚ˆă‚‹ćčČ枉:ćŒ· ă‚ćˆă†è§’ φmax⁥=arcsin⁥(nλ/d),n∈Z.I∝\varphi_{\max }=\arcsin (n \lambda / d), n \in \mathbb{Z} . I \propto cos⁥2(ka2sinâĄÏ†),(k=2π/λ)\cos ^2\left(k \frac{a}{2} \sin \varphi\right),(k=2 \pi / \lambda)

7.3: 捘ă‚čăƒȘット-ćŒ±ă‚ćˆă†è§’

  1. 捘ă‚čăƒȘット:ćŒ±ă‚ćˆă†è§’: φmin =arcsin⁥(nλ/d),n∈\varphi_{\text {min }}=\arcsin (n \lambda / d), n \in Z,n≠0\mathbb{Z}, n \neq 0. äž­ć€źăźćŒ·ă‚ćˆă†éƒšćˆ†ăŻ n=±1n=\pm 1 ぼ間である ă“ăšă«æłšæ„ă›ă‚ˆ. I∝sin⁥2(kd2sinâĄÏ†)/sinâĄÏ†I \propto \sin ^2\left(k \frac{d}{2} \sin \varphi\right) / \sin \varphi

7.4: ć›žæŠ˜æ Œć­

  1. ć›žæŠ˜æ Œć­ïŒšäž»ăȘćŒ·ă‚ćˆă†è§’ăŻăƒă‚€ăƒłăƒˆ 2 べ搌じで, äž» ăȘćŒ·ă‚ćˆă†è§’ăźćč…は dd ă‚’ć›žæŠ˜æ Œć­ăźæ­Łć‘łăźé•·ă•ăšă™ă‚Œ ă°ăƒă‚€ăƒłăƒˆ 3 べ搌じ. nn ç•Șç›źăźæ˜Žç·šăźă‚čăƒšă‚Żăƒˆăƒ«ăźćˆ† è§ŁèƒœăŻïŒŒæșăźç·æ•°ă‚’ NN æœŹăšă—ăŠ λΔλ=nN\frac{\lambda}{\Delta \lambda}=n N.

7.5: ćˆ†ć…‰ć™šăźćˆ†è§Łèƒœ

  1. ćˆ†ć…‰ć™šăźćˆ†è§Łèƒœ : æœ€çŸ­ăźć…‰ç·šăšæœ€é•·ăźć…‰ç·šăźć…‰ć­Šè·é›ą た淟を LL べしど, λΔλ=Lλ\frac{\lambda}{\Delta \lambda}=\frac{L}{\lambda}.

7.6: プăƒȘă‚șăƒ ăźćˆ†è§Łèƒœ

  1. プăƒȘă‚șăƒ ăźćˆ†è§Łèƒœ :λΔλ=adn dλ: \frac{\lambda}{\Delta \lambda}=a \frac{\mathrm{d} n}{\mathrm{~d} \lambda}

7.7: 角ćșŠè·é›ą

  1. ç†æƒłçš„ăȘæœ›é éĄ (ハンă‚ș) で 2 ç‚čă‚’è§Łćƒă™ă‚‹ăšăăźè§’ćșŠè·é›ą : φ≈1.22λ/d\varphi \approx 1.22 \lambda / d. ă“ăźè§’ćșŠă§ăŻ, 侀æ–čたç‚čた䞭 ćżƒăŒä»–æ–čたç‚čăźæœ€ćˆăźć›žæŠ˜æœ€ć°ć€Œă«ćœ“ăŸă‚‹.

7.8: Bragg ăźæł•ć‰‡

  1. Bragg ăźæł•ć‰‡ïŒšé–“éš”ăŒ dd たćčłèĄŒăȘç”æ™¶éąăźç”„ăŻ, 2dsin⁥Ξ=nλ2 d \sin \theta=n \lambda ăȘらば X\mathrm{X} ç·šă‚’ćć°„ă™ă‚‹. ここで Ξ\theta は甐 æ™¶éąăš X ç·šăŒăȘă™è§’ (ă‹ă™ă‚è§’).

7.9: é«˜ćŻ†ćșŠé›»äœ“ćȘ’èłȘ揍氄

  1. ć…‰ć­Šçš„ă«é«˜ćŻ†ćșŠăȘèȘ˜é›»äœ“ćȘ’èłȘă«ă‚ˆă‚‹ćć°„ : äœç›žăŒ π\pi ず れる. ćŠé€æ˜Žăźè–„è†œă§ăŻ ϕ→+ϕ←=π\phi_{\rightarrow}+\phi_{\leftarrow}=\pi. ここで ϕ→\phi_{\rightarrow} ず ϕ←\phi_{\leftarrow} ăŻćć°„æłąăšé€éŽæłąăźäœç›žć·źïŒˆçŸąć°ăŻć…„ć°„æ–č搑を ç€șす)

7.10: Fabry-PĂ©rot ćčČ枉蚈

  1. Fabry-PĂ©rot ćčČ枉蚈 : é«˜ă„ćć°„çŽ‡ r(1−râ‰Ș1)r(1-r \ll 1) ă‚’æŒ ぀ 2 æžšăźćčłèĄŒăȘćŠé€æ˜ŽăźéĄ. ćˆ†è§ŁèƒœăŻ ΜΔΜ≈2aλ(1−r)\frac{\nu}{\Delta \nu} \approx \frac{2 a}{\lambda(1-r)}. 5 ぀たćčłéąæłą (ćčČæž‰èšˆăźć‰ă§ć·Šćłă«é€Čă‚€æłą, ć†…éƒšă‚’ć·Šćł にé€Čă‚€æłąïŒŒćŸŒă‚ă‚’é€Čă‚€æłąïŒ‰ă‚’èš­ćźšă—ăŠćąƒç•ŒæĄä»¶ă‚’èȘČす ă“ăšă§ïŒŒé€éŽă‚čăƒšă‚Żăƒˆăƒ«ă‚’æ±‚ă‚ă‚‰ă‚Œă‚‹.

7.11: ă‚łăƒ’ăƒŒăƒŹăƒłăƒˆăȘé›»çŁæłą

  1. ă‚łăƒ’ăƒŒăƒŹăƒłăƒˆăȘé›»çŁæłą: é›»ć Žă‚’ăƒ™ă‚Żăƒˆăƒ«äžșă§èĄšă—, ベク ăƒˆăƒ«é–“ăźè§’ćșŠă‚’äœç›žć·źăšă™ă‚‹. ć±ˆæŠ˜çŽ‡ăŒ n=n(ω)=n=n(\omega)= Δ(ω)\sqrt{\varepsilon(\omega)} (æ™źé€š Ό≈1\mu \approx 1 ) ă§ă‚ă‚‹ă“ăšă«æłšæ„ă›ă‚ˆ. スネ ăƒ«ă‚źăƒŒæ”ćŻ†ćșŠïŒˆć˜äœéąç©ă‚’é€šéŽă™ă‚‹ć˜äœæ™‚é–“ă‚ăŸă‚Šăź ă‚šăƒăƒ«ă‚źăƒŒïŒ‰: I=cnΔ0E2=cnÎŒ0B2(EI=c n \varepsilon_0 E^2=\frac{c}{n \mu_0} B^2(E ず BB は漟 ćŠčć€Œ)

7.12: Malus ăźæł•ć‰‡

  1. Malus ăźæł•ć‰‡ : ç›Žç·šćć…‰ăŒè§’ćșŠ φ\varphi ă§ćć…‰æżă‚’é€šéŽă™ă‚‹ ず I=I0cos⁥2φI=I_0 \cos ^2 \varphi

7.13: 1/4 æłąé•·ç‰ˆ

  1. 1/41 / 4 æłąé•·ç‰ˆ : ç›Žç·šćć…‰æˆćˆ†é–“ăźäœç›žăŒ π/2\pi / 2 ずれる.

7.14: Brewster 角

  1. Brewster 角: ć…„ć°„è§’ăŒ tanâĄÏ†=n\tan \varphi=n をæș€ăŸă™ăšă, 揍 ć°„æłąăšć±ˆæŠ˜æłąăŒćž‚ç›Žă«ăȘă‚Šćć°„æłąăŻç›Žç·šćć…‰ăšăȘる.

7.15: ć…‰ć­ŠçŽ ć­ă«ă‚ˆă‚‹ć›žæŠ˜

  1. ć…‰ć­ŠçŽ ć­ă«ă‚ˆă‚‹ć›žæŠ˜ : ハンă‚șやプăƒȘă‚șムăȘどを通る慉 ăźć…‰ć­Šè·é›ąă‚’èšˆçź—ă™ă‚‹ćż…èŠăŻăȘく, ć›łćœąçš„ă«è€ƒăˆă‚‹. äŸ‹ăˆă°ïŒŒćŒăƒ—ăƒȘă‚șムはäșŒé‡ă‚čăƒȘăƒƒăƒˆă«ă‚ˆă‚‹ć›žæŠ˜ăšćŒă˜ ć›žæŠ˜ă‚’ă™ă‚‹.

7.16: ć…‰ăƒ•ă‚Ąă‚€ăƒăƒŒ supplemental

  1. ć…‰ăƒ•ă‚Ąă‚€ăƒăƒŒïŒšMach-Zehnder ćčČæž‰èšˆăŻäșŒé‡ă‚čăƒȘッ ăƒˆă«ă‚ˆă‚‹ćčČæž‰ăš, ć††ćœąć…±æŒŻć™šăŻ Fabry-PĂ©rot ćčČ枉蚈 ăšäŒŒăŠă„ă‚‹. Bragg ăƒ•ă‚Łăƒ«ă‚żăƒŒăŻ X\mathrm{X} ç·šăźć ŽćˆăšćŒ ă˜ă‚ˆă†ă«ćƒă. ă‚·ăƒłă‚°ăƒ«ăƒąăƒŒăƒ‰ăźć…‰ăƒ•ă‚Ąă‚€ăƒăƒŒă§ăŻ, Δn/n≈12(λ/d)2\Delta n / n \approx \frac{1}{2}(\lambda / d)^2.
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/8.html b/academic/physics/ipho-formulas-jpn/8.html new file mode 100644 index 00000000..97f47b1a --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/8.html @@ -0,0 +1,61 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 8 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 8

8: é›»æ°—ć›žè·Ż

8.1: V=I R, P=V I

  1. V=IR,P=VIV=I R, P=V I

    R目戗 =∑Ri,R侩戗 −1=∑Ri−1R_{\text {目戗 }}=\sum R_i, R_{\text {侩戗 }}^{-1}=\sum R_i^{-1}

8.2: Kirchhoff ăźæł•ć‰‡

  1. Kirchhoff ăźæł•ć‰‡ :

    ∑ 節ç‚č I=0,âˆ‘é–‰è·ŻÂ V=0\sum_{\substack{\text { 節ç‚č }}} I=0, \sum_{\text {é–‰è·Ż }} V=0

8.3: ăƒă‚€ăƒłăƒˆ 2 たæ–čçš‹ćŒă‚’æž›ă‚‰ă™ăŸă‚ă«

  1. ăƒă‚€ăƒłăƒˆ 2 たæ–čçš‹ćŒă‚’æž›ă‚‰ă™ăŸă‚ă«: 節ç‚čé›»äœæł•. ăƒ«ăƒŒ ăƒ—é›»æ”æł•. ç­‰äŸĄć›žè·Ż (3 端歐た栎搈 ⇒△揈\Rightarrow \triangle 揈 揈 YY ăźćœą, è”·é›»ćŠ›ăźă‚ă‚‹ 2 端歐た栎搈 ⇒\Rightarrow æŠ”æŠ—ăšé›»æ± ăźç›Žćˆ—)

8.4: 焥限に぀ăȘăŒă‚‹æŠ”æŠ—

  1. 焥限に぀ăȘăŒă‚‹æŠ”æŠ— : ç„Ąé™ă«ç¶šăæ Œć­ăźéšŁă‚Šćˆă†çŻ€ç‚č é–“ă§ïŒŒè‡Șć·±ç›žäŒŒæ€§ă‚’äœżă†ă€‚éĄćƒæł•ăźäž€èˆŹćŒ–ă•ă‚ŒăŸæ–čæł•.

8.5: äș€æ”ć›žè·Ż

  1. äș€æ”ć›žè·Ż: RR を ZZ ă«çœźăæ›ăˆăŠăƒă‚€ăƒłăƒˆ 1∌41 \sim 4 を甹 いる.

    ZR=R,ZC=1/iωC,ZL=iωLφ=arg⁥Z,Veff =∣Z∣Ieff P=∣V∣∣I∣cos⁥(arg⁥Z)=∑Ii2Ri\begin{gathered} Z_R=R, Z_C=1 / i \omega C, Z_L=i \omega L \\ \varphi=\arg Z, V_{\text {eff }}=|Z| I_{\text {eff }} \\ P=|V||I| \cos (\arg Z)=\sum I_i^2 R_i \end{gathered}

8.6: ç‰č性時間

  1. ç‰č性時間: τRC=RC,τLR=L/R.ωLC=\tau_{R C}=R C, \tau_{L R}=L / R . \omega_{L C}= 1/LC1 / \sqrt{L C}. 漚澾的ăȘé›»æ”ćˆ†ćžƒăžăźç·©ć’ŒăŻæŒ‡æ•°é–ąæ•°çš„ă§ ∝e−t/τ\propto e^{-t / \tau}

8.7: é›»æ°—ć›žè·Żăźă‚šăƒăƒ«ă‚źăƒŒäżć­˜ć‰‡

  1. é›»æ°—ć›žè·Żăźă‚šăƒăƒ«ă‚źăƒŒäżć­˜ć‰‡ : ΔW+Q=qV\Delta W+Q=q V. ここ で qq ăŻé›»ćœ§é™äž‹ VV ă‚’é€šăŁăŸé›»æ°—é‡ă§, 電æșăźă™ă‚‹ä»•äș‹ は A=qVemfA=q V_{\mathrm{emf}}

8.8: ă‚łăƒłăƒ‡ăƒłă‚”ăƒŒăźäœçœźă‚šăƒăƒ«ă‚źăƒŒćŒ

  1. ă‚łăƒłăƒ‡ăƒłă‚”ăƒŒăźäœçœźă‚šăƒăƒ«ă‚źăƒŒćŒ: WC=CV2/2,WL=LI2/2W_C=C V^2 / 2, W_L=L I^2 / 2.

8.9: çŁæŸćŻ†ćșŠ

  1. Vemf=−dΩ/dt=d(LI)/dt,Ω=BSV_{\mathrm{emf}}=-\mathrm{d} \Phi / \mathrm{d} t=\mathrm{d}(L I) / \mathrm{d} t, \Phi=B S.

8.10: éžç·šćœąçŽ ć­

  1. 非 ç·šćœąçŽ ć­: V−IV-I ă‚°ăƒ©ăƒ•ă§ăźéžç·šćœąæ›Č線ず Ohm/Kirchhoff ăźæł•ć‰‡ă‚’èĄšă™ç›Žç·šăšăźäș€ç‚čべしど äžșćœąçš„ă«è§Łă‚’æ±‚ă‚ă‚‹. è€‡æ•°ăźäș€ç‚čăŒă‚ă‚Œă°ćź‰ćźšæ€§ă‚’èȘż ベる. ă„ăă€ă‹ăźè§ŁăŻæ™źé€šćź‰ćźšă§ăȘい.

8.11: çŸ­æ™‚é–“ăšé•·æ™‚é–“ăźæ„”é™ă‚’ćˆ©ç”š

  1. çŸ­æ™‚é–“ăšé•·æ™‚é–“ăźæ„”é™ă‚’ćˆ©ç”šă™ă‚‹: tobservation ≫t_{\text {observation }} \gg τRC\tau_{R C} or τLR\tau_{L R} ăȘらば, IC≈0(CI_C \approx 0(C ăŻæ–­ç·šă—ăŠă„ă‚‹ïŒ‰ćˆ は VL≈0V_L \approx 0 ( LL ăŻçŸ­ç”Ąă—ăŠă„ă‚‹ïŒ‰ăźă‚ˆă†ăȘæș–ćčłèĄĄçŠ¶æ…‹ă« 達する. tobservation â‰ȘτRCt_{\text {observation }} \ll \tau_{R C} or τLR\tau_{L R} ăȘらば, CC た電 æ°—é‡ăźć€‰ćŒ–ă‚„ LL ă§ăźé›»æ”ăźć€‰ćŒ–ăŻć°ă•ă, ΔQâ‰ȘQ\Delta Q \ll Q や ΔIâ‰ȘI\Delta I \ll I. 捳ち CC ăŻçŸ­ç”Ąă—ăŠă„ăŠ LL ăŻæ–­ç·šă—ăŠ いる.

8.12: 掚論

  1. L≠0L \neq 0 ăȘらば, I(t)I(t) は連続.

8.13: è¶…é›»ć°Žăźć›žè·Ż

  1. è¶…é›»ć°Žăźć›žè·Żă«ă€ă„ăŠ, çŁæŸ Ί=\Phi= const.. ç‰čに, ć€–éƒš 磁栮が無ければ LI=L I= const.

8.14: 盾äș’èȘ˜ć°Ž

  1. 盾äș’èȘ˜ć°Ž : ć›žè·Ż 1 ă‚’é€šă‚‹çŁæŸăŻ Ί1=L1I1+L12I2\Phi_1=L_1 I_1+L_{12} I_2 ( I2I_2 ăŻć›žè·Ż 2 ă‚’æ”ă‚Œă‚‹é›»æ”) で, L12=L21≡ML_{12}=L_{21} \equiv M ず M≀L1L2M \leq \sqrt{L_1 L_2} ăŒæˆç«‹.
+ + + + + \ No newline at end of file diff --git a/academic/physics/ipho-formulas-jpn/9.html b/academic/physics/ipho-formulas-jpn/9.html new file mode 100644 index 00000000..3fd33cdf --- /dev/null +++ b/academic/physics/ipho-formulas-jpn/9.html @@ -0,0 +1,39 @@ + + + + + + Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 9 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 9

9: é›»çŁæ°—ć­Š

9.1: Coulomb ăźæł•ć‰‡

  1. F=kq1q2/r2,U=kq1q2/rF=k q_1 q_2 / r^2, U=k q_1 q_2 / r で, Kepler ăźæł•ć‰‡ăŒ äœżăˆă‚‹ (Section 12 揂照).

9.2: Gauss ăźæł•ć‰‡

  1. Gauss ăźæł•ć‰‡ : ∟B⋅dS=0\oint \boldsymbol{B} \cdot \mathrm{d} \boldsymbol{S}=0,

    ∟ΔE⋅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: ćŸȘ環漚理

  1. ćŸȘ環漚理 :

    ∟E⋅dl=0(=Ω˙),∟B⋅dlÎŒ=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: é›»æ”çŽ ç‰‡ă«ă‚ˆă‚Šç”Ÿă˜ă‚‹çŁæŸćŻ†ćșŠ

  1. é›»æ”çŽ ç‰‡ă«ă‚ˆă‚Šç”Ÿă˜ă‚‹çŁæŸćŻ†ćșŠ :

    dB=ÎŒI4πdl×err2.\mathrm{d} \boldsymbol{B}=\frac{\mu I}{4 \pi} \frac{\mathrm{d} \boldsymbol{l} \times \boldsymbol{e}_r}{r^2} .

    ă—ăŸăŒăŁăŠé›»æ” II ăŒæ”ă‚Œă‚‹ć††ćœąć›žè·Żăźäž­ćżƒă§ăŻ B=ÎŒ0I2rB=\frac{\mu_0 I}{2 r}.

9.5: ăƒ­ăƒŒăƒŹăƒłăƒ„ćŠ›

  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 ぼ漚理べćŸȘ環漚理より

  1. Gauss ぼ漚理べćŸȘç’°ćźšç†ă‚ˆă‚ŠïŒšćžŻé›»ă—ăŸć°Žç·šă«ă€ă„ăŠ E=σ2πΔ0rE=\frac{\sigma}{2 \pi \varepsilon_0 r}, é›»æ”ăŒæ”ă‚Œă‚‹ć°Žç·šă«ă€ă„ăŠ B=ÎŒ0I2πrB=\frac{\mu_0 I}{2 \pi r}. ćžŻé›»ă—ăŸéąă«ă€ă„ăŠ E=σ2Δ0E=\frac{\sigma}{2 \varepsilon_0}, é›»æ”ăŒæ”ă‚Œă‚‹éąă«ă€ă„ お B=ÎŒ0i2B=\frac{\mu_0 i}{2}. äž€æ§˜ă«ćžŻé›»ă—ăŸçƒæźŒïŒˆćˆăŻç„Ąé™ă«é•·ă„ć†† ç­’ïŒ‰ăźć†…éƒšă§ E=0E=0, è»žă«æČżăŁăŠèĄšéąă«é›»æ”ăŒæ”ă‚Œă‚‹ 憆筒ぼ憅郹で B=0B=0. 毆ćșŠ ρ\rho ă§äž€æ§˜ă«ćžŻé›», ćˆăŻäž€æ§˜ ăȘ電攁 i\boldsymbol{i} ăŒæ”ă‚Œă‚‹, 球 (d=3)/(d=3) / ć††æŸ± (d−2)/(d-2) / ćčłéą (d=1)(d=1) ぼ憅郹で,

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

9.7: é•·ă„ă‚œăƒŹăƒŽă‚€ăƒ‰

  1. é•·ă„ă‚œăƒŹăƒŽă‚€ăƒ‰: 憅郹で B=ÎŒnIB=\mu n I, ć€–éƒšă§ B=0B=0. çŁæŸ Ί=NBS(n=Nl)\Phi=N B S\left(n=\frac{N}{l}\right). ă‚€ăƒłăƒ€ă‚Żă‚żăƒłă‚č L=L= Ί/I=ÎŒn2V\Phi / I=\mu n^2 V. çŸ­ă„ă‚œăƒŹăƒŽă‚€ăƒ‰ :B∄=ÎŒnIΩ4π(Ω: B_{\|}=\frac{\mu n I \Omega}{4 \pi}(\Omega は 立䜓角).

9.8: çŁć Žă‚’ć°ćž‹ă‚łă‚€ăƒ«ă‚„èĄæ’ƒæ€œæ”èšˆă§æžŹćźšă™ă‚‹

  1. çŁć Žă‚’ć°ćž‹ă‚łă‚€ăƒ«ă‚„èĄæ’ƒæ€œæ”èšˆă§æžŹćźšă™ă‚‹ïŒš q=q= ∫VR dt=NSΔB/R\int \frac{V}{R} \mathrm{~d} t=N S \Delta B / R.

9.9: é™é›»ć Žăźă‚šăƒăƒ«ă‚źăƒŒ

  1. é™é›»ć Žăźă‚šăƒăƒ«ă‚źăƒŒïŒš

    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: äž€æ§˜ă«ćžŻé›»ă—ăŸçƒéąă‚„ć††ç­’éąăźć„éƒšćˆ†ăźé–“ă«ćƒăćŠ›

  1. äž€æ§˜ă«ćžŻé›»ă—ăŸçƒéąă‚„ć††ç­’éąăźć„éƒšćˆ†ăźé–“ă«ćƒăćŠ› : ćžŻé›»ă«ă‚ˆă‚‹ćŠ›ă‚’é™æ°Žćœ§ă«ă‚ˆă‚‹ćŠ›ă«çœźăæ›ăˆă‚‹.

9.11: ć…šăŠăźé›»è·

  1. ć…šăŠăźé›»è·ăŒè·é›ą rr ă«ă‚ă‚‹ć ŽćˆïŒˆäŸ‹ăˆă°ïŒŒäžć‡äž€ă«ćžŻ é›»ă—ăŸçƒă‚„ăƒȘăƒłă‚°ăźäž­ćżƒïŒ‰ ϕϕ=kQ/r\phi \phi=k Q / r

9.12: ć€–éƒšé›»è·

  1. ć€–éƒšé›»è·ă«ă‚ˆăŁăŠćŒ•ăè”·ă“ă•ă‚Œă‚‹æ­Łć‘łăźé›»è·ïŒˆćˆăŻé›» äœïŒ‰ă‚’æ±‚ă‚ă‚‹ă«ăŻ, é›»è·ă‚’ă€Œć‡șçŸă€ă•ă›ăŠć•éĄŒă‚’ćŻŸç§°çš„ ă«ă—ïŒŒé‡ă­ćˆă‚ă›ăźćŽŸç†ă‚’ç”šă„ă‚‹.

9.14: ć°Žäœ“

  1. ć°Žäœ“ăŻé›»è·ă‚„é›»ć Žă‚’éźè”œă™ă‚‹ïŒŽäŸ‹ăˆă°ïŒŒäž­ç©șăźçƒäœ“ăź ć†…éƒšăźé›»è·ćˆ†ćžƒăŻć€–ă‹ă‚‰èŠ‹ăˆăȘă„ïŒˆă‚ăŸă‹ă‚‚ QQ べいう é›»è·ă‚’æŒăŁăŸć°Žé›»æ€§ăźçƒăŒă‚ă‚‹ă‚ˆă†ă«èŠ‹ăˆă‚‹).

9.15: 静電ćźč量

  1. 静電ćźč量: C=ΔS/dC=\varepsilon S / d (ćčłæż), 4πΔr4 \pi \varepsilon r (球), 2πΔl(ln⁥R/r)−12 \pi \varepsilon l(\ln R / r)^{-1} (ćŒè»žć††ç­’).

9.16: ćŒæ„”ć­ăƒąăƒŒăƒĄăƒłăƒˆ

  1. ćŒæ„”ć­ăƒąăƒŒăƒĄăƒłăƒˆïŒš

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

9.17: ćŒæ„”ć­ć Ž

  1. ćŒæ„”ć­ć Ž : 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: ćŒæ„”ć­ă«ćƒăćŠ›

  1. ćŒæ„”ć­ă«ćƒăćŠ› : F=(pe⋅E)â€Č,F=(pΌ⋅B)â€ČF=\left(\boldsymbol{p}_e \cdot \boldsymbol{E}\right)^{\prime}, F=\left(\boldsymbol{p}_\mu \cdot \boldsymbol{B}\right)^{\prime} [èšł è€…æłš : ă“ă“ăźćŸźćˆ†ăŻă‚€ă—ă‚ grad⁥\operatorname{grad} である]. 2 ă€ăźćŒæ„” 歐間ぼ盾äș’䜜甚 :F∝r−4: F \propto r^{-4}.

9.19: çŁæ°—ćŒæ„”ć­ăšă—ăŠăźç‚č電荷

  1. çŁæ°—ćŒæ„”ć­ăšă—ăŠăźç‚č電荷 : pΌ∝Ί∝v⊄2/Bp_\mu \propto \Phi \propto v_{\perp}^2 / B ăŻæ–­ç†± äžć€‰é‡ (Section 4: #22 揂照).

9.20: éĄćƒæł•

  1. éĄćƒæł• : æŽ„ćœ°ă•ă‚ŒăŸïŒˆçŁçŸłăźć ŽćˆăŻè¶…é›»ć°ŽăźïŒ‰ćčłéąăŒéĄ たćœčć‰Čをする. æŽ„ćœ°ă•ă‚ŒăŸïŒˆćˆăŻć­€ç«‹ă—ăŸïŒ‰çƒäœ“ăźć Ž は, çƒäœ“ăźć†…éƒšă«ă‚ă‚‹ 1 ă€ïŒˆćˆăŻ 2 ă€ïŒ‰ăźæž¶ç©șăźé›»è· ăźă€ăă‚‹ć Žăšă—ăŠæ±‚ă‚ă‚‰ă‚Œă‚‹. ćčłéąć°ŽæłąçźĄïŒˆé‡‘ć±žæżăź 間ぼă‚čăƒȘăƒƒăƒˆïŒ‰ć†…ăźć ŽăŻ, 電磁ćčłéąæłąăźé‡ă­ćˆă‚ă›ăš ă—ăŠæ±‚ă‚ă‚‰ă‚Œă‚‹.

9.21: äž€æ§˜ïŒˆé›»ïŒ‰ć Žäž­ăźçƒ (ć††æŸ±) ăźćˆ†æ„”

  1. äž€æ§˜ïŒˆé›»ïŒ‰ć Žäž­ăźçƒ (ć††æŸ±) ăźćˆ†æ„” : (+ρ(+\rho ず −ρ-\rho に䞀 æ§˜ă«ćžŻé›»ă—ăŸçƒ (ć††æŸ±) ăźé‡ă­ćˆă‚ă›ă§ïŒŒ d∝Ed \propto E.

9.22: 枊電攁

  1. 枊電攁: é›»æ”æć€±ćŻ†ćșŠ ≈B2v2/ρ.1\approx B^2 v^2 / \rho .1 曞ぼ通過で侎え られる運拕量 : Fτ≈B2a3d/ρF \tau \approx B^2 a^3 d / \rho (ここで dd は掚さ, aa ăŻć€§ăă•).
+ + + + + \ No newline at end of file diff --git a/academic/vocabulary/2023/02/2023-02-27.html b/academic/vocabulary/2023/02/2023-02-27.html new file mode 100644 index 00000000..33568f2d --- /dev/null +++ b/academic/vocabulary/2023/02/2023-02-27.html @@ -0,0 +1,39 @@ + + + + + + 2023-2-27: Vocabulary | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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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

+ + + + + \ No newline at end of file diff --git a/academic/vocabulary/index.html b/academic/vocabulary/index.html new file mode 100644 index 00000000..74a37327 --- /dev/null +++ b/academic/vocabulary/index.html @@ -0,0 +1,39 @@ + + + + + + Welcome to My Vocabulary List! | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Welcome to My Vocabulary List!

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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:

',4),r=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("mn",null,"2"),s("msub",null,[s("mi",{mathvariant:"normal"},"C"),s("mn",null,"8")]),s("msub",null,[s("mi",{mathvariant:"normal"},"H"),s("mn",null,"18")]),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"normal"},"l"),s("mo",{stretchy:"false"},")"),s("mo",null,"+"),s("mn",null,"25"),s("msub",null,[s("mi",{mathvariant:"normal"},"O"),s("mn",null,"2")]),s("mo",{stretchy:"false"},"("),s("mrow",null,[s("mtext",null," "),s("mi",{mathvariant:"normal"},"g")]),s("mo",{stretchy:"false"},")"),s("mo",null,"⟶"),s("mn",null,"16"),s("msub",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"C"),s("mi",{mathvariant:"normal"},"O")]),s("mn",null,"2")]),s("mo",{stretchy:"false"},"("),s("mrow",null,[s("mtext",null," "),s("mi",{mathvariant:"normal"},"g")]),s("mo",{stretchy:"false"},")"),s("mo",null,"+"),s("mn",null,"18"),s("msub",null,[s("mi",{mathvariant:"normal"},"H"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"O"),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"normal"},"g"),s("mo",{stretchy:"false"},")")]),s("annotation",{encoding:"application/x-tex"},"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}) ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"2"),s("span",{class:"mord"},[s("span",{class:"mord mathrm"},"C"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3011em"}},[s("span",{style:{top:"-2.55em","margin-left":"0em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord 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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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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 æ—„æœŹèȘžç‰ˆ: Section 1

1: æ•°ć­Š

1.1: Taylor 汕開

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")])])]),s("span",{class:"vlist-s"},"​")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"5.7102em"}},[s("span")])])])])])])])])])])])])],-1),k=l('

1.8: ć††ć‘šè§’

  1. ć††ć‘šè§’ăŻäž­ćżƒè§’ăźćŠćˆ†. ă‚ˆăŁăŠïŒŒç›Žè§’äž‰è§’ćœąăźæ–œèŸșは ăăźć€–æŽ„ć††ăźç›ŽćŸ„. ă‚‚ă—ć››è§’ćœąăźćŻŸè§’ăźć’ŒăŒ 180 ćșŠăȘ ă‚‰ă°ïŒŒăă‚ŒăŻć††ă«ć†…æŽ„ă™ă‚‹.

1.9: äž‰è§’ćœąăźéąæš

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 11

11: 量歐抛歩

11.1:p=hk

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11.2: ćčČ枉

  1. ćčČ枉 : æłąć‹•ć…‰ć­Šăźă‚ˆă†ă«.

11.3: 䞍çąșćźšæ€§

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diff --git a/assets/academic_physics_ipho-formulas-jpn_12.md.b9360cda.js b/assets/academic_physics_ipho-formulas-jpn_12.md.b9360cda.js new file mode 100644 index 00000000..db7e3912 --- /dev/null +++ b/assets/academic_physics_ipho-formulas-jpn_12.md.b9360cda.js @@ -0,0 +1 @@ +import{_ as e,o as n,c as m,a as s,b as a,e as i,d as l,r}from"./app.6caaf9fc.js";const F=JSON.parse('{"title":"Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 12","description":"","frontmatter":{},"headers":[{"level":2,"title":"12: Kepler ăźæł•ć‰‡","slug":"_12-kepler-ăźæł•ć‰‡","link":"#_12-kepler-ăźæł•ć‰‡","children":[{"level":3,"title":"12.1: F & U","slug":"_12-1-f-u","link":"#_12-1-f-u","children":[]},{"level":3,"title":"12.2: Kepler ăźçŹŹäž€æł•ć‰‡","slug":"_12-2-kepler-ăźçŹŹäž€æł•ć‰‡","link":"#_12-2-kepler-ăźçŹŹäž€æł•ć‰‡","children":[]},{"level":3,"title":"12.3: Kepler た珏äșŒæł•ć‰‡","slug":"_12-3-kepler-た珏äșŒæł•ć‰‡","link":"#_12-3-kepler-た珏äșŒæł•ć‰‡","children":[]},{"level":3,"title":"12.4: Kepler ăźçŹŹäž‰æł•ć‰‡","slug":"_12-4-kepler-ăźçŹŹäž‰æł•ć‰‡","link":"#_12-4-kepler-ăźçŹŹäž‰æł•ć‰‡","children":[]},{"level":3,"title":"12.5: æ„•ć††è»Œé“","slug":"_12-5-æ„•ć††è»Œé“","link":"#_12-5-æ„•ć††è»Œé“","children":[]},{"level":3,"title":"12.6: æ„•ć††çŽ‡","slug":"_12-6-æ„•ć††çŽ‡","link":"#_12-6-æ„•ć††çŽ‡","children":[]},{"level":3,"title":"12.7: æ„•ć††ăźæ€§èłȘ","slug":"_12-7-æ„•ć††ăźæ€§èłȘ","link":"#_12-7-æ„•ć††ăźæ€§èłȘ","children":[]},{"level":3,"title":"12.8: 憆ぼ侭濃","slug":"_12-8-憆ぼ侭濃","link":"#_12-8-憆ぼ侭濃","children":[]},{"level":3,"title":"12.9: nge-Lenz ăƒ™ă‚Żăƒˆăƒ«","slug":"_12-9-nge-lenz-ăƒ˜ă‚™ă‚Żăƒˆăƒ«","link":"#_12-9-nge-lenz-ăƒ˜ă‚™ă‚Żăƒˆăƒ«","children":[]}]}],"relativePath":"academic/physics/ipho-formulas-jpn/12.md","lastUpdated":1677686831000}'),p={name:"academic/physics/ipho-formulas-jpn/12.md"},c=l('

Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 12

12: Kepler ăźæł•ć‰‡

12.1: F & U

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12.2: Kepler ăźçŹŹäž€æł•ć‰‡

  1. Kepler ăźçŹŹäž€æł•ć‰‡ (2 èłȘç‚čぼ重抛盾äș’䜜甚)ïŒšăă‚Œăž ă‚Œăźè»Œé“ăŻïŒŒçł»ăźèłȘé‡äž­ćżƒă«ç„Šç‚čă‚’æŒă€æ„•ć††ïŒŒćŒæ›Č線, æ”Ÿç‰©ç·šă«ăȘる. これは Runge-Lenz ăƒ™ă‚Żăƒˆăƒ«ă‹ă‚‰ćŸ—ă‚‰ れる (ăƒă‚€ăƒłăƒˆ 9).

12.3: Kepler た珏äșŒæł•ć‰‡

  1. Kepler た珏äșŒæł•ć‰‡ïŒˆè§’é‹ć‹•é‡ăźäżć­˜ïŒ‰: 侭濃抛が惍く 栎にあるèłȘç‚čă«ă€ă„ăŠïŒŒăăźäœçœźăƒ™ă‚Żăƒˆăƒ«ăŻć˜äœæ™‚é–“ ă«äž€ćźšăźéąç©ă‚’æă.

12.4: Kepler ăźçŹŹäž‰æł•ć‰‡

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 13

13: ç›žćŻŸæ€§ç†è«–

13.1:Lorentz ć€‰æ›

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 3

3: 運拕歩

3.1: èłȘç‚č

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3.3: æ›Č線運拕

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3.4: ć‰›äœ“ăźé‹ć‹•

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3.7: æœ€çŸ­ç”Œè·Ż

  1. æœ€çŸ­ç”Œè·Żă‚’æ±‚ă‚ă‚‹ă«ăŻïŒŒFermat ず Huygens ぼ掟理が äœżăˆă‚‹.

3.8: ăƒ™ă‚Żăƒˆăƒ«

  1. ăƒ™ă‚Żăƒˆăƒ«ïŒˆé€ŸćșŠïŒŒćŠ é€ŸćșŠïŒ‰ă‚’æ±‚ă‚ă‚‹ă«ăŻïŒŒăăźć‘ăăš ïŒˆć Žćˆă«ă‚ˆăŁăŠăŻć‚Ÿă„ăŸïŒ‰ă‚ă‚‹è»žăžăźć°„ćœ±ă‚’æ±‚ă‚ă‚Œă° 慅戆.
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ć‰›äœ“ăźă™ăčどぼ運拕","slug":"_4-17-ć‰›äœ“ăźă™ăžă‚™ăŠăźé‹ć‹•","link":"#_4-17-ć‰›äœ“ăźă™ăžă‚™ăŠăźé‹ć‹•","children":[]},{"level":3,"title":"4.18: çŽăźćŒ”ćŠ›","slug":"_4-18-çŽăźćŒ”ćŠ›","link":"#_4-18-çŽăźćŒ”ćŠ›","children":[]},{"level":3,"title":"4.19: æ¶Čäœ“ăźèĄšéą","slug":"_4-19-æ¶Čäœ“ăźèĄšéą","link":"#_4-19-æ¶Čäœ“ăźèĄšéą","children":[]},{"level":3,"title":"4.20: éžćœ§çžźæ€§æ”äœ“ă«ćŻŸă™ă‚‹ Bernoulli ăźæł•ć‰‡","slug":"_4-20-éžćœ§çžźæ€§æ”äœ“ă«ćŻŸă™ă‚‹-bernoulli-ăźæł•ć‰‡","link":"#_4-20-éžćœ§çžźæ€§æ”äœ“ă«ćŻŸă™ă‚‹-bernoulli-ăźæł•ć‰‡","children":[]},{"level":3,"title":"4.21: 盎線的ăȘ攁線","slug":"_4-21-盎線的ăȘ攁線","link":"#_4-21-盎線的ăȘ攁線","children":[]},{"level":3,"title":"4.22: æ–­ç†±äžć€‰é‡","slug":"_4-22-æ–­ç†±äžć€‰é‡","link":"#_4-22-æ–­ç†±äžć€‰é‡","children":[]},{"level":3,"title":"4.23: ćź‰ćźšæ€§","slug":"_4-23-ćź‰ćźšæ€§","link":"#_4-23-ćź‰ćźšæ€§","children":[]},{"level":3,"title":"4.24: ç©șé–“çš„ă«æœ‰é™ăȘé‹ć‹•ă«ćŻŸă™ă‚‹ Virial 漚理","slug":"_4-24-ç©șé–“çš„ă«æœ‰é™ăȘé‹ć‹•ă«ćŻŸă™ă‚‹-virial-漚理","link":"#_4-24-ç©șé–“çš„ă«æœ‰é™ăȘé‹ć‹•ă«ćŻŸă™ă‚‹-virial-漚理","children":[]},{"level":3,"title":"4.25: Tsiolkovsky ć…ŹćŒ","slug":"_4-25-tsiolkovsky-ć…ŹćŒ","link":"#_4-25-tsiolkovsky-ć…ŹćŒ","children":[]}]}],"relativePath":"academic/physics/ipho-formulas-jpn/4.md","lastUpdated":1677686831000}'),r={name:"academic/physics/ipho-formulas-jpn/4.md"},c=n('

Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 4

4: 抛歩

4.1: ć‰›äœ“ăźäșŒæŹĄć…ƒçš„ăȘćčłèĄĄ

  1. ć‰›äœ“ăźäșŒæŹĄć…ƒçš„ăȘćčłèĄĄ : 抛に぀いおた 2 ă€ăźćŒăšăƒˆăƒ« クに぀いおた 1 ă€ăźćŒ. 1 ïŒˆćˆăŻ 2 ïŒ‰ć€‹ăźćŠ›ă«ă€ă„ăŠăź ćŒăŻ 1ïŒˆćˆăŻ 2ïŒ‰ć€‹ăźăƒˆăƒ«ă‚Żă«ă€ă„ăŠăźćŒă§ä»Łç”šă§ă る. ăƒˆăƒ«ă‚Żăźæ–čăŒè‰Żă„ć ŽćˆăŒć€šăïŒŒćŽŸç‚čă‚’é©ćˆ‡ă«éžæŠž ă™ă‚‹ă“ăšă§ă€Œé€€ć±ˆăȘă€ćŠ›ă‚’æ¶ˆă™ă“ăšăŒă§ăă‚‹. もし 2 ç‚č ăźăżă«ćŠ›ăŒă‹ă‹ăŁăŠă„ă‚‹ăȘă‚‰ă°ïŒŒïŒˆæ­Łć‘łăźïŒ‰ćŠ›ăŒă‹ă‹ăŁ ăŠă„ă‚‹ç›Žç·šăŻäž€è‡Žă™ă‚‹. 3 ç‚čであれば, 3 ぀た盎線は 1 ç‚čでäș€ă‚ă‚‹.

4.2: ćž‚ç›ŽæŠ—ćŠ›

',5),h=s("ol",{start:"2"},[s("li",null,[a("ćž‚ç›ŽæŠ—ćŠ›ăšæ‘©æ“ŠćŠ›ăŻ 1 ă€ăźćŠ›ă«ćˆæˆă§ă, ćž‚ç›ŽæŠ—ćŠ›ă« ćŻŸă—ăŠ "),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,"arctan"),s("mo",null,"⁥"),s("mi",null,"ÎŒ")]),s("annotation",{encoding:"application/x-tex"},"\\arctan \\mu")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8095em","vertical-align":"-0.1944em"}}),s("span",{class:"mop"},"arctan"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal"},"ÎŒ")])])]),a(" ăźè§’ćșŠă§æŽ„觊ç‚čă«ćŠ ă‚ă‚‹.")])],-1),o=s("h3",{id:"_4-3-䞊é€Čé‹ć‹•ăšć›žè»ąé‹ć‹•",tabindex:"-1"},[a("4.3: 䞊é€Čé‹ć‹•ăšć›žè»ąé‹ć‹• 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た珏äșŒæł•ć‰‡ïŒš"),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",{mathvariant:"bold-italic"},"F"),s("mo",null,"="),s("mi",null,"m"),s("mi",{mathvariant:"bold-italic"},"a"),s("mo",{separator:"true"},","),s("mi",{mathvariant:"bold-italic"},"M"),s("mo",null,"="),s("mi",null,"I"),s("mi",{mathvariant:"bold-italic"},"Δ"),s("mspace",{width:"1em"}),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"bold-italic"},"M"),s("mo",null,"="),s("mi",{mathvariant:"bold-italic"},"r"),s("mo",null,"×"),s("mi",{mathvariant:"bold-italic"},"F"),s("mo",{stretchy:"false"},")")]),s("annotation",{encoding:"application/x-tex"},"\\boldsymbol{F}=m \\boldsymbol{a}, \\boldsymbol{M}=I \\boldsymbol{\\varepsilon} \\quad(\\boldsymbol{M}=\\boldsymbol{r} \\times \\boldsymbol{F}) 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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,"M")]),s("annotation",{encoding:"application/x-tex"},"M")])])]),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":"0.10903em"}},"M")])])]),a(" ず "),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,"Δ")]),s("annotation",{encoding:"application/x-tex"},"\\varepsilon")])])]),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"},"Δ")])])]),a(" ăŻæœŹèłȘ的にă‚čă‚«ăƒ©ăƒŒă§, "),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,"M"),s("mo",null,"="),s("mi",null,"F"),s("mi",null,"l"),s("mo",null,"="),s("msub",null,[s("mi",null,"F"),s("mi",null,"t")]),s("mi",null,"r"),s("mo",{stretchy:"false"},"("),s("mi",null,"l")]),s("annotation",{encoding:"application/x-tex"},"M=F l=F_t r(l")])])]),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":"0.10903em"}},"M"),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:"0.6944em"}}),s("span",{class:"mord 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4.13: ă‚ˆăäœżă‚ă‚Œă‚‹äżć­˜ć‰‡

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 5

5. æŒŻć‹•ăšæłą

5.1: æž›èĄ°æŒŻć‹•

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 6

6: ćčŸäœ•ć…‰ć­ŠïŒŒæžŹć…‰

6.1: Fermat 掟理

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  1. ćƒăźäœçœźă‚’æ±‚ă‚ă‚‹èŠ–ć·źæł• : ç›źăźäœçœźăšćž‚ç›Žă«ć‹•ă‹ă—ăŸ ăšăă«ïŒŒé‰›ç­†ăźć…ˆăŒćƒă«ćŻŸă—ăŠăšă‚ŒăȘいようăȘäœçœźă‚’ æŽąă™.

6.8: ハンă‚șă‚’é€šă‚‹ć…‰ç·šăźç”Œè·ŻăźćčŸäœ•ć­Šçš„ăȘæăæ–č

  1. ハンă‚șă‚’é€šă‚‹ć…‰ç·šăźç”Œè·ŻăźćčŸäœ•ć­Šçš„ăȘæăæ–ča) ハン ă‚șăźäž­ćżƒă‚’é€šă‚‹ć…‰ç·šăŻć±ˆæŠ˜ă—ăȘい。b) ć…‰è»žă«ćčłèĄŒăȘ慉 線は焊ç‚čă‚’é€šă‚‹ïŒŒc) ć±ˆæŠ˜ćŸŒ, ćˆă‚ă«ćčłèĄŒă ăŁăŸć…‰ç·šă©ă†ă—は焊ç‚čéąïŒˆç„Šç‚čă‚’é€šă‚Šć…‰è»žă«ćž‚ç›ŽăȘćčłéąïŒ‰äžŠă§é›† ăŸă‚‹ïŒŽd) ćčłéąăźćƒăŻćčłéąă§ă‚ă‚ŠïŒŒă“ăź 2 ぀たćčłéąăŻăƒŹ ンă‚șたćčłéąäžŠă§äș€ă‚ă‚‹ïŒŽ

6.9: ć…‰æŸ

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 7

7: æłąć‹•ć…‰ć­Š

7.1: Huygens ăźćŽŸç†ă«ćŸșă„ă„ăŸć›žæŠ˜

  1. Huygens ăźćŽŸç†ă«ćŸșă„ă„ăŸć›žæŠ˜ : éšœćźłç‰©ăŒæłąéąă‚’ćˆ‡æ–­ ă™ă‚‹ăšæłąéąăŻć°ă•ăȘæ–­ç‰‡ă«ćˆ†ć‰Čă•ă‚ŒïŒŒăă‚ŒăŒä»źæƒłçš„ăȘ ç‚čæłąæșăšăȘă‚ŠïŒŒèŠłæžŹç‚čă§ăźæłąăźæŒŻćč…ăŻă“ă‚Œă‚‰ăźæłąæșă‹ らぼ毄侎ぼ重ね搈わせべăȘる.

7.2: äșŒé‡ă‚čăƒȘット

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 8

8: é›»æ°—ć›žè·Ż

8.1: V=I R, P=V I

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8.4: 焥限に぀ăȘăŒă‚‹æŠ”æŠ—

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8.5: äș€æ”ć›žè·Ż

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Formulas for IPhO æ—„æœŹèȘžç‰ˆ: Section 9

9: é›»çŁæ°—ć­Š

9.1: Coulomb ăźæł•ć‰‡

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\\sum_{i9.10: äž€æ§˜ă«ćžŻé›»ă—ăŸçƒéąă‚„ć††ç­’éąăźć„éƒšćˆ†ăźé–“ă«ćƒăćŠ›
  1. äž€æ§˜ă«ćžŻé›»ă—ăŸçƒéąă‚„ć††ç­’éąăźć„éƒšćˆ†ăźé–“ă«ćƒăćŠ› : ćžŻé›»ă«ă‚ˆă‚‹ćŠ›ă‚’é™æ°Žćœ§ă«ă‚ˆă‚‹ćŠ›ă«çœźăæ›ăˆă‚‹.

9.11: ć…šăŠăźé›»è·

',3),B=s("ol",{start:"12"},[s("li",null,[a("ć…šăŠăźé›»è·ăŒè·é›ą "),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(" ă«ă‚ă‚‹ć ŽćˆïŒˆäŸ‹ăˆă°ïŒŒäžć‡äž€ă«ćžŻ é›»ă—ăŸçƒă‚„ăƒȘăƒłă‚°ăźäž­ćżƒïŒ‰ "),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: ć€–éƒšé›»è·

  1. ć€–éƒšé›»è·ă«ă‚ˆăŁăŠćŒ•ăè”·ă“ă•ă‚Œă‚‹æ­Łć‘łăźé›»è·ïŒˆćˆăŻé›» äœïŒ‰ă‚’æ±‚ă‚ă‚‹ă«ăŻ, é›»è·ă‚’ă€Œć‡șçŸă€ă•ă›ăŠć•éĄŒă‚’ćŻŸç§°çš„ ă«ă—ïŒŒé‡ă­ćˆă‚ă›ăźćŽŸç†ă‚’ç”šă„ă‚‹.

9.14: ć°Žäœ“

',3),I=s("ol",{start:"14"},[s("li",null,[a("ć°Žäœ“ăŻé›»è·ă‚„é›»ć Žă‚’éźè”œă™ă‚‹ïŒŽäŸ‹ăˆă°ïŒŒäž­ç©șăźçƒäœ“ăź ć†…éƒšăźé›»è·ćˆ†ćžƒăŻć€–ă‹ă‚‰èŠ‹ăˆăȘă„ïŒˆă‚ăŸă‹ă‚‚ "),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(" べいう é›»è·ă‚’æŒăŁăŸć°Žé›»æ€§ăźçƒăŒă‚ă‚‹ă‚ˆă†ă«èŠ‹ăˆă‚‹).")])],-1),S=s("h3",{id:"_9-15-静電ćźč量",tabindex:"-1"},[a("9.15: 静電ćźč量 "),s("a",{class:"header-anchor",href:"#_9-15-静電ćźč量","aria-hidden":"true"},"#")],-1),E=s("ol",{start:"15"},[s("li",null,[a("静電ćźč量: 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r^{-4}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mrel"},":"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),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:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 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B")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7167em","vertical-align":"-0.2861em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"p"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.1514em"}},[s("span",{style:{top:"-2.55em","margin-left":"0em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"ÎŒ")])])]),s("span",{class:"vlist-s"},"​")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2861em"}},[s("span")])])])])]),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:"0.6833em"}}),s("span",{class:"mord"},"Ί"),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:"1.0972em","vertical-align":"-0.2831em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"v"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t 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9.20: éĄćƒæł•

  1. éĄćƒæł• : æŽ„ćœ°ă•ă‚ŒăŸïŒˆçŁçŸłăźć ŽćˆăŻè¶…é›»ć°ŽăźïŒ‰ćčłéąăŒéĄ たćœčć‰Čをする. æŽ„ćœ°ă•ă‚ŒăŸïŒˆćˆăŻć­€ç«‹ă—ăŸïŒ‰çƒäœ“ăźć Ž は, çƒäœ“ăźć†…éƒšă«ă‚ă‚‹ 1 ă€ïŒˆćˆăŻ 2 ă€ïŒ‰ăźæž¶ç©șăźé›»è· ăźă€ăă‚‹ć Žăšă—ăŠæ±‚ă‚ă‚‰ă‚Œă‚‹. ćčłéąć°ŽæłąçźĄïŒˆé‡‘ć±žæżăź 間ぼă‚čăƒȘăƒƒăƒˆïŒ‰ć†…ăźć ŽăŻ, 電磁ćčłéąæłąăźé‡ă­ćˆă‚ă›ăš ă—ăŠæ±‚ă‚ă‚‰ă‚Œă‚‹.

9.21: äž€æ§˜ïŒˆé›»ïŒ‰ć Žäž­ăźçƒ (ć††æŸ±) ăźćˆ†æ„”

',3),j=s("ol",{start:"21"},[s("li",null,[a("äž€æ§˜ïŒˆé›»ïŒ‰ć Žäž­ăźçƒ (ć††æŸ±) ăźćˆ†æ„” : "),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("mo",{stretchy:"false"},"("),s("mo",null,"+"),s("mi",null,"ρ")]),s("annotation",{encoding:"application/x-tex"},"(+\\rho")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mopen"},"("),s("span",{class:"mord"},"+"),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" ず 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.1")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4831em"}}),s("span",{class:"mrel"},"≈"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mord"},[s("span",{class:"mord 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\\rho")])])]),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":"0.13889em"}},"F"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.1132em"}},"τ"),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:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),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:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},"3")])])])])])])]),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" (ここで "),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,"d")]),s("annotation",{encoding:"application/x-tex"},"d")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathnormal"},"d")])])]),a(" は掚さ, "),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:"0.4306em"}}),s("span",{class:"mord mathnormal"},"a")])])]),a(" ăŻć€§ăă•).")])],-1),U=[i,r,p,c,h,o,g,d,u,y,v,b,x,w,_,k,z,M,f,B,L,I,S,E,q,T,F,V,N,P,C,R,A,j,G,Q];function D(O,$,J,K,H,W){return n(),m("div",null,U)}const Z=t(e,[["render",D]]);export{Y as __pageData,Z as default}; diff --git a/assets/academic_physics_ipho-formulas-jpn_9.md.72ec3a76.lean.js b/assets/academic_physics_ipho-formulas-jpn_9.md.72ec3a76.lean.js new file mode 100644 index 00000000..a4cc72d9 --- /dev/null +++ b/assets/academic_physics_ipho-formulas-jpn_9.md.72ec3a76.lean.js @@ -0,0 +1 @@ +import{_ as t,o as n,c as m,d as l,a as s,b as a}from"./app.6caaf9fc.js";const 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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

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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
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Values of the number type are numeric values, normally written as follows,

js
144
+
144
+

TIP

But the standard describes JavaScript numbers as 64-bit floating-point values, which indicates fractions and exponents are available.

`,4),m=s("p",null,[e("Not all whole numbers "),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("mn",null,"1"),s("msup",null,[s("mn",null,"0"),s("mn",null,"19")])]),s("annotation",{encoding:"application/x-tex"},"10^{19}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},"1"),s("span",{class:"mord"},[s("span",{class:"mord"},"0"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"19")])])])])])])])])])])]),e(" fit in a JavaScript number. There are also negative numbers, so one of the bits has to be used to store the sign of the number.")],-1),y=s("ul",null,[s("li",null,"11 bits are used to store the position of the decimal dot within the number."),s("li",null,[e("52 bits, any whole number less than "),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("mn",null,"2"),s("mn",null,"52")])]),s("annotation",{encoding:"application/x-tex"},"2^{52}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"2"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"52")])])])])])])])])])])]),e(", which is more than "),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("mn",null,"1"),s("msup",null,[s("mn",null,"0"),s("mn",null,"15")])]),s("annotation",{encoding:"application/x-tex"},"10^{15}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},"1"),s("span",{class:"mord"},[s("span",{class:"mord"},"0"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"15")])])])])])])])])])])]),e(" will safely fit in a JavaScript number, numbers we are using stay well below that.")])],-1),b=a(`

Fractional numbers are written by using a dot,

js
9.81
+
9.81
+

For extreme huge or tiny numbers, we can also use "scientific" notion by adding an e, followed by the exponent of the number,

js
2.998e8
+
2.998e8
+
`,4),g=s("p",null,[e("This indicates "),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("mn",null,"2.998"),s("mo",null,"×"),s("mn",null,"1"),s("msup",null,[s("mn",null,"0"),s("mn",null,"8")]),s("mo",null,"="),s("mn",null,"29980000")]),s("annotation",{encoding:"application/x-tex"},"2.998 \\times 10^8 = 29980000")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7278em","vertical-align":"-0.0833em"}}),s("span",{class:"mord"},"2.998"),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:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},"1"),s("span",{class:"mord"},[s("span",{class:"mord"},"0"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},"8")])])])])])])]),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:"0.6444em"}}),s("span",{class:"mord"},"29980000")])])]),e(".")],-1),C=s("p",null,[e("Calculations with whole numbers (referred as "),s("em",null,"integers"),e(") that fits into 52 bits are guaranteed to be always precise, but calculation with fraction numbers are generally not.")],-1),v=s("ul",null,[s("li",null,[e("Such as "),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,"π")]),s("annotation",{encoding:"application/x-tex"},"\\pi")])])]),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":"0.03588em"}},"π")])])]),e(" cannot be precisely expressed by a finite amount of decimal digits, "),s("strong",null,"thus many numbers lose some precision when only 64 bits are available to store them.")])],-1),w=s("details",{class:"details custom-block"},[s("summary",null,"1-1-1: Numbers review"),s("ul",null,[s("li",null,[e("64 bits: A 64-bit number is a binary sequence of 64 bits, which can represent "),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("mn",null,"2"),s("mn",null,"64")])]),s("annotation",{encoding:"application/x-tex"},"2^{64}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"2"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"64")])])])])])])])])])])]),e(" (18,446,744,073,709,551,616) different values. This is commonly used for representing memory addresses and integers with large values in computer systems.")]),s("li",null,[e("11 bits: An 11-bit number is a binary sequence of 11 bits, which can represent "),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("mn",null,"2"),s("mn",null,"11")])]),s("annotation",{encoding:"application/x-tex"},"2^{11}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"2"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"11")])])])])])])])])])])]),e(" (2,048) different values. This is often used in computer systems for encoding small integers, such as color values in images.")]),s("li",null,[e("52 bits: A 52-bit number is a binary sequence of 52 bits, which can represent "),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("mn",null,"2"),s("mn",null,"52")])]),s("annotation",{encoding:"application/x-tex"},"2^{52}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"2"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[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 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"52")])])])])])])])])])])]),e(" (4,503,599,627,370,496) different values. This is often used for representing the significand or mantissa portion of a floating-point number in computer systems.")])])],-1),k=a(`

1-1-2: Arithmetic

The main thing to do with numbers is arithmetic. Arithmetic operations such as addition or multiplication take two number values and produce a new number from them, the following is an example of calculation in JavaScript.

js
100 + 4 * 11
+
100 + 4 * 11
+

  • The + and * symbols are called operators.

    • + apparently stands for addition while * stands for multiplication.

  • This expression indicates the multiplication takes place first then the adding of 100 comes next as a regard to PEMDAS rules (Order of Operations).

But we can still overwrite the steps of operation using a parenthesis around the addition,

js
;(100 + 4) * 11
+
;(100 + 4) * 11
+

For subtraction, there is the - operator, and division can be done with /. When operators appear together without parentheses, they are applied is determined by the precedence of the operators.

  • When multiple operators with the same precedence appear next to each other (as 1-2+1), they are applied left to right (refers to PEMDAS).
  • Precedence: Priorities.

WARNING

When is doubt, don't care about precedence, just add parentheses for order of operation.

There is one more arithmetic operator, which is the % percent sign used to represent the modulo operation. The term "X modulo Y" is defined as the remainder of dividing X by Y.

  • For example, 314 % 100 is 14, 10 % 3 is 1, and 144 % 12 is 0 because there are no remainders.
  • Modulo's precedence is the same as that of multiplication and division.
1-2: Arithmetic review
  • All of the operators in JavaScript follows precedence rules, or referred as PEMDAS in conventional math.
    • + and - has the same lowest precedence.
    • * , / and % has the same medium precedence.
    • () has the highest precedence, followed on with brackets.
  • The symbol % refers to "modulo", in mathematical reading, we say "X modulo Y" is the remainder of X over Y.

1-1-3: Strings

The next data type is the string. Its use is not as evident from its name as with numbers, it also fulfills a very basic role.

  • Strings are used to represent text.
  • Strings are usually written by enclosing the contents with quotes.
js
'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+
'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+

TIP

Both single and double quotes can be used to mark strings

  • As long as the quotes at the start and the end of the string match.

Almost anything can be put between quotes, and JavaScript will make a string value out of it. But the followings are tricky to be put between quotes.

  • Newlines: The things we get when we press enter on keyboard. We uses \\n to represent.
  • New tab: Similarly like newlines, \\t indicates a new tab being indented.

Take the following string as an example,

js
'Lorem ipsum dolor sit amet,\\n consectetur adipiscing elit.'
+
'Lorem ipsum dolor sit amet,\\n consectetur adipiscing elit.'
+

The following will be the rendered output,

js
Lorem ipsum dolor sit amet,
+consectetur adipiscing elit.
+
Lorem ipsum dolor sit amet,
+consectetur adipiscing elit.
+

WARNING

But the situations where we want a backslash in a string to just be a backslash instead of a special code. By using \\\\ would render the "just slash" to \\ on output, instead of a special character, as follows,

js
"A newline character is written like \\"\\\\n\\"."
+
"A newline character is written like \\"\\\\n\\"."
+

Strings cannot be divided, multiplied, or subtracted, unlike integers. But the + operator can be used on the. It concatenates (glues) the two strings together, the following example will produce the string "concatenate".

js
'con' + 'cat' + 'e' + 'nate'
+
'con' + 'cat' + 'e' + 'nate'
+
1-1-3: Strings review
  • Nearly everything could be put into strings in JavaScript
  • String could be wrapped with "" double quotation marks or '' single quotation marks.
  • There is a tricky situation in JavaScript's string, where \\ backslash followed with a character are being introduced specially by the interpreter, such as \\n referred as newline, \\t referred as new tab.
    • \\\\ double backslash will be rendered as a single \\.
    • \\& symbols followed after slash will not contain its original function such as connecting, but will be rendered as & on output.

1-1-3-FR: Further Reading

From the example given in the prior section with a lot of backslashes, it might be hard to understand the concept on at what time the slash will be rendered and when it will be considered as a special character starter.

The example is given as,

js
"A newline character is written like \\"\\\\n\\"."
+
"A newline character is written like \\"\\\\n\\"."
+

The rendered output will be on print,

js
A newline character is written like "\\n".
+
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)

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Theme

Homepage

  • [x] 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

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

Configs

  • [ ] Header configs including different properties and meta configs.
  • [ ] Complete navigation configuration.
    • [ ] Navigation divider and text title, line breakings.
  • [ ] 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
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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

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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

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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 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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var(--vp-c-divider-light);padding-top:24px;letter-spacing:-.02em;line-height:32px;font-size:24px} diff --git a/getting-started.html b/getting-started.html new file mode 100644 index 00000000..65c70b50 --- /dev/null +++ b/getting-started.html @@ -0,0 +1,53 @@ + + + + + + Git push results in "Authentication Failed” | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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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/hashmap.json b/hashmap.json new file mode 100644 index 00000000..c7e6d8f6 --- /dev/null +++ b/hashmap.json @@ -0,0 +1 @@ +{"academic_chemistry_notes_12-5.md":"e500c017","academic_physics_ipho-formulas-jpn_2.md":"8b3002e5","academic_physics_ipho-formulas-jpn_3.md":"03ebd227","academic_physics_ipho-formulas-jpn_5.md":"ed720adf","academic_physics_ipho-formulas-jpn_6.md":"a605b6cc","academic_vocabulary_index.md":"cafce8dc","getting-started.md":"962994a9","index.md":"03313a33","javascript_notes_1_1-1.md":"59b97c74","javascript_notes_1_1-2.md":"653a34cc","academic_physics_ipho-formulas-jpn_13.md":"ac17556a","academic_physics_ipho-formulas-jpn_11.md":"17e80ffd","academic_physics_ipho-formulas-jpn_12.md":"b9360cda","roadmap.md":"2c4e5f92","save_reading_index.md":"6f5fa8f5","save_reading_outliers_1.md":"658b4dbe","save_reading_outliers_2.md":"6ed52866","save_reading_outliers_3.md":"5b43dc39","save_reading_outliers_4.md":"8ad99116","academic_physics_ipho-formulas-jpn_10.md":"4f21e572","academic_literature_index.md":"65702726","academic_physics_index.md":"c37369d0","academic_vocabulary_2023_02_2023-02-27.md":"1db2e1a6","academic_literature_writing_methods-of-development.md":"b1416ac2","academic_chemistry_presentation-problems_pp-2-20.md":"197f9146","academic_physics_ipho-formulas-jpn_4.md":"42e164d0","academic_physics_ipho-formulas-jpn_7.md":"823a932a","academic_physics_ipho-formulas-jpn_8.md":"595fe489","academic_chemistry_index.md":"bbfc8844","academic_physics_ipho-formulas-jpn_1.md":"e180b6fa","academic_physics_ipho-formulas-jpn_9.md":"72ec3a76"} diff --git a/index.html b/index.html new file mode 100644 index 00000000..67228e81 --- /dev/null +++ b/index.html @@ -0,0 +1,39 @@ + + + + + + Toshiki's Notebook | Eternal digital knowledge base for content craetion and notes management. + + + + + + + + + + + + + + + + + + + + + + + + + + +
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1-1: Values

1-1-1: Numbers must know

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
+

  • With the following bash script, 144 will be converted into binary values in integer form,

    sh
    ip1=144 # defines a variable named ip1, with the value of 10
+echo "obase=2;$ip1" | bc # convert the value to binary via bc
+
    ip1=144 # defines a variable named ip1, with the value of 10
+echo "obase=2;$ip1" | bc # convert the value to binary via bc
+
    • The variable ip1 is assigned the value 144.
    • The echo command prints out the string "obase=2;144", where "obase=2;" is an argument for bc that tells it to output the result in base 2 (binary), and "10" is the decimal number we want to convert.
    • The output of the echo command is piped (using the | character) to bc, which takes the input "obase=2;144" and interprets it as a command to convert the number 10 to binary.
    • Finally, the binary equivalent of 144, which is "10010000", is printed to the terminal.

TIP

But the standard describes JavaScript numbers as 64-bit floating-point values, which indicates fractions and exponents are available.

Not all whole numbers 101910^{19} fit in a JavaScript number. There are also negative numbers, so one of the bits has to be used to store the sign of the number.

  • 11 bits are used to store the position of the decimal dot within the number.
  • 52 bits, any whole number less than 2522^{52}, which is more than 101510^{15} will safely fit in a JavaScript number, numbers we are using stay well below that.

Fractional numbers are written by using a dot,

js
9.81
+
9.81
+

For extreme huge or tiny numbers, we can also use "scientific" notion by adding an e, followed by the exponent of the number,

js
2.998e8
+
2.998e8
+

This indicates 2.998×108=299800002.998 \times 10^8 = 29980000.

Calculations with whole numbers (referred as integers) that fits into 52 bits are guaranteed to be always precise, but calculation with fraction numbers are generally not.

  • Such as π\pi cannot be precisely expressed by a finite amount of decimal digits, thus many numbers lose some precision when only 64 bits are available to store them.
1-1-1: Numbers review
  • 64 bits: A 64-bit number is a binary sequence of 64 bits, which can represent 2642^{64} (18,446,744,073,709,551,616) different values. This is commonly used for representing memory addresses and integers with large values in computer systems.
  • 11 bits: An 11-bit number is a binary sequence of 11 bits, which can represent 2112^{11} (2,048) different values. This is often used in computer systems for encoding small integers, such as color values in images.
  • 52 bits: A 52-bit number is a binary sequence of 52 bits, which can represent 2522^{52} (4,503,599,627,370,496) different values. This is often used for representing the significand or mantissa portion of a floating-point number in computer systems.

1-1-2: Arithmetic

The main thing to do with numbers is arithmetic. Arithmetic operations such as addition or multiplication take two number values and produce a new number from them, the following is an example of calculation in JavaScript.

js
100 + 4 * 11
+
100 + 4 * 11
+

  • The + and * symbols are called operators.

    • + apparently stands for addition while * stands for multiplication.

  • This expression indicates the multiplication takes place first then the adding of 100 comes next as a regard to PEMDAS rules (Order of Operations).

But we can still overwrite the steps of operation using a parenthesis around the addition,

js
;(100 + 4) * 11
+
;(100 + 4) * 11
+

For subtraction, there is the - operator, and division can be done with /. When operators appear together without parentheses, they are applied is determined by the precedence of the operators.

  • When multiple operators with the same precedence appear next to each other (as 1-2+1), they are applied left to right (refers to PEMDAS).
  • Precedence: Priorities.

WARNING

When is doubt, don't care about precedence, just add parentheses for order of operation.

There is one more arithmetic operator, which is the % percent sign used to represent the modulo operation. The term "X modulo Y" is defined as the remainder of dividing X by Y.

  • For example, 314 % 100 is 14, 10 % 3 is 1, and 144 % 12 is 0 because there are no remainders.
  • Modulo's precedence is the same as that of multiplication and division.
1-2: Arithmetic review
  • All of the operators in JavaScript follows precedence rules, or referred as PEMDAS in conventional math.
    • + and - has the same lowest precedence.
    • * , / and % has the same medium precedence.
    • () has the highest precedence, followed on with brackets.
  • The symbol % refers to "modulo", in mathematical reading, we say "X modulo Y" is the remainder of X over Y.

1-1-3: Strings

The next data type is the string. Its use is not as evident from its name as with numbers, it also fulfills a very basic role.

  • Strings are used to represent text.
  • Strings are usually written by enclosing the contents with quotes.
js
'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+
'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+'Lorem ipsum dolor sit amet, consectetur adipiscing elit.'
+

TIP

Both single and double quotes can be used to mark strings

  • As long as the quotes at the start and the end of the string match.

Almost anything can be put between quotes, and JavaScript will make a string value out of it. But the followings are tricky to be put between quotes.

  • Newlines: The things we get when we press enter on keyboard. We uses \n to represent.
  • New tab: Similarly like newlines, \t indicates a new tab being indented.

Take the following string as an example,

js
'Lorem ipsum dolor sit amet,\n consectetur adipiscing elit.'
+
'Lorem ipsum dolor sit amet,\n consectetur adipiscing elit.'
+

The following will be the rendered output,

js
Lorem ipsum dolor sit amet,
+consectetur adipiscing elit.
+
Lorem ipsum dolor sit amet,
+consectetur adipiscing elit.
+

WARNING

But the situations where we want a backslash in a string to just be a backslash instead of a special code. By using \\ would render the "just slash" to \ on output, instead of a special character, as follows,

js
"A newline character is written like \"\\n\"."
+
"A newline character is written like \"\\n\"."
+

Strings cannot be divided, multiplied, or subtracted, unlike integers. But the + operator can be used on the. It concatenates (glues) the two strings together, the following example will produce the string "concatenate".

js
'con' + 'cat' + 'e' + 'nate'
+
'con' + 'cat' + 'e' + 'nate'
+
1-1-3: Strings review
  • Nearly everything could be put into strings in JavaScript
  • String could be wrapped with "" double quotation marks or '' single quotation marks.
  • There is a tricky situation in JavaScript's string, where \ backslash followed with a character are being introduced specially by the interpreter, such as \n referred as newline, \t referred as new tab.
    • \\ double backslash will be rendered as a single \.
    • \& symbols followed after slash will not contain its original function such as connecting, but will be rendered as & on output.

1-1-3-FR: Further Reading

From the example given in the prior section with a lot of backslashes, it might be hard to understand the concept on at what time the slash will be rendered and when it will be considered as a special character starter.

The example is given as,

js
"A newline character is written like \"\\n\"."
+
"A newline character is written like \"\\n\"."
+

The rendered output will be on print,

js
A newline character is written like "\n".
+
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)

+ + + + + \ No newline at end of file diff --git a/javascript/notes/1/1-2.html b/javascript/notes/1/1-2.html new file mode 100644 index 00000000..bb7f3294 --- /dev/null +++ b/javascript/notes/1/1-2.html @@ -0,0 +1,39 @@ + + + + + + 1-2 | Toshiki's Note + + + + + + + + + + + + + + + + + + + + + + + + + + +
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TOC
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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

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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

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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 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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