OpenLLM-France/wikimedia huggingface dataset:
# Cascading Style Sheets/Lengths and Units

To specify widths, heights and other lengths, you can use various units, listed in the following table.
Units in CSS :
| Code | Definition |
| em | The height of the element's font. |
| rem | The height of the browser font size. |
| ex | The height of the letter 'x' in the element's font. |
| px | pixel |
| mm | millimeter |
| cm | centimeter |
| pt | point (1/72 inch) |
| pc | pica (12 points = 1/6 inch) |
| in | inch |
| vw | 1/100 of a viewport's width |
| vh | 1/100 of a viewport's height |
Lengths may also be specified as a percentage of another length. Using percentages can be complicated because the base length varies from property to property. For example, when percentages are used with the margin property the calculation is based on the width of the containing block. When percentages are used with the font-size property the calculation is based on the font-size of the parent element but with line-height it is based on the font-size of the current element.
Font sizes on screen are best given as a percentage or in ems. (See the note on Using ems in Internet Explorer.) This means that the page will interact gracefully with users' font preferences. Using pixels (px) for font sizes causes a number of problems and should be avoided.
The absolute units mm, cm, pt, pc and in do not work well on screen and cause problems in many older browsers. It is safest to only use them for print media. Even in print media they may interact badly with users' preferences.

## Relative units

The three units em, ex and px are called relative units. These units do not specify a fixed length. Instead they scale relative to some other quantity. In the case of em and ex they scale relative to the font size of some element.

### Screen pixels, printer pixels and CSS pixels

The px unit specifies a length in CSS pixels. These are not the same as the pixels on the screen that the document is rendered on or the dots on the printer that it is printed on. It is perfectly possible, for example, for there to be two screen pixels or five printer dots to one CSS pixel. Many web browsers use the rule that one screen pixel equals one CSS pixel for simplicity but you can not rely on this. Opera and Internet Explorer version 7 allow the user to change the number of screen pixels per CSS pixel. It is common for users with poor vision who use these browsers to choose to have five or six screen pixels to the CSS pixel.
The formal definition of the CSS pixel is quite complicated but the basic idea is that a CSS pixel appears to be the same size when the document is at a comfortable reading distance. So a CSS pixel would be physically bigger on a monitor than on a mobile phone because the monitor would normally be further from the user's eyes than the mobile phone.

### Calculations

Divide the desired margin width/height by the width/height of its container to convert it to ems. Multiply by 100 to convert that to percentages.
Divide the desired container width by 1.62 to use the Golden Ratio as the size of the content block. Subtract the content width from the container width to use the Golden Ratio as the size of the sidebar
# Wikijunior
### Welcome to Wikijunior!

The aim of this project is to produce age-appropriate non-fiction books for children from birth to age 12. These books are richly illustrated with photographs, diagrams, sketches, and original drawings. Wikijunior books are produced by a worldwide community of writers, teachers, students, and young people all working together. The books present factual information that is verifiable. You are invited to join in and write, edit, and rewrite each book and chapter to improve its content. Our books are distributed free of charge under the terms of the Creative Commons Attribution-ShareAlike License.
Please see What is Wikijunior? for more information about the project.
Search Wikijunior:

### Titles

There are more than a dozen Wikijunior books and hundreds of sections within those books being readied for publication.

#### Discovery and innovation

The Elements — Fun Science Experiments — How Things Work

#### The natural world

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Ancient Civilizations — Kings and Queens of England — Languages — United States Charters of Freedom — World War II — World at Work

#### Geography

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#### School time

Geometry for Elementary School

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Alphabet — Animal Alphabet — Object Alphabet — Classic Alphabet Coloring Book — Colors — Flower Alphabet — Food Alphabet — Maze & Drawing Book — Numbers from 1 to 20 — Small Numbers — Skateboard Alphabet Coloring Pages — Tell Time Clock Coloring Book — Transport Alphabet — Valentines Hearts Alphabet Coloring Book
Additional Wikijunior books are under development.

### All for KIDS

Wikijunior has some great books for you to read. But you can also help by writing books! If you know something about a subject and want to share it with others, just click on the link that says "edit" and type in what you want to say. It's that easy!

### Helping out

It's easy to get started. Just click on an edit button and begin writing! We encourage you to be bold and edit articles.
If you want ideas on what to do, you can consider:
* Look through our full collection of books and add content where you can.
* Start a class project to write a new book or contribute to an existing, developing one.
* Tell us how we're doing on the talk page.
* Fact-check a page.
* Check articles for grammar, style, and spelling.
* Monitor the recent changes to Wikijunior pages.
There's a Wikijunior Style Guide with suggestions for how to write great Wikijunior content.

### Discussions

You can discuss the project at the Wikijunior talk page or one of the Wikibooks reading rooms to get a broader audience.
To chat about Wikijunior on IRC, use Freenode or join #wikibooks on Freenode.
# Algebra/Chapter 1/Review

In this chapter, you learned about the fundamental concepts of arithmetic necessary for understanding algebra.

## 1.1 - The Number Line

The are many different types of numbers.
# Algebra/Chapter 23/Polynomial Roots
## Theory of equations

A Fundamental subject in Mathematics, which deals with the methods of finding roots of a given mathematical expression.Suppose f(x) is a function in x and m is a constant in the range of the function.Now if :-
,there are only a finite number of values of x which can satisfy the given expression. Of course this is not true for trigonometric equations which yield an infinite number of roots but usually only the principal values of angles are taken.

## Solution to a Quadratic equation

Theoretically a polynomial equation of the nth degree can be resolved into n factors.Let us consider the polynomial equation:-
let us assume F(x)=(x-m)(x-n)(x-o)(x-p).................. where m,n are called the roots of the equation F(x). Now if we multiply the factors we obtain:- $F(x)=x^{n}-(m+n+o......)x^{n-1}+(mn+no+.........)x^{n-2}................+mnop......$ Comparing with the polymomial,
This identity was discovered by Vieta and is named after him. Hence we have n equations to find n roots. Now consider an equation of degree 2 called the Quadratic equation.Let m,n be the roots of the equation. Let the equation be :-
This can also be written as:- $x^{2}+{\frac {bx}{a}}+{\frac {c}{a}}=0$ dividing by a
From the above treatise we know that:-
# Algebra/Chapter 1/Factoring and Divisibility

| Exponents and Roots | Algebra Chapter 1: Elementary Arithmetic Section 4: Factoring and Divisibility | Integers |
1.4: Factoring and Divisibility
By now, I hope you are familiar with the addition, subtraction, multiplication, and exponentiation of whole numbers. Division of whole numbers, however, works a little differently from the other three operators. This is because you can not always divide integers evenly.
# Algebra/Chapter 1/Fractions

| Integers | Algebra Chapter 1: Elementary Arithmetic Section 6: Fractions | Decimals |
1.6: Fractions

## Division with Fractions

* Keep first fraction
* Find the reciprocal of the second
* Multiply the two new fractions.
# Algebra/Chapter 1/Integers

| Factoring and Divisibility | Algebra Chapter 1: Elementary Arithmetic Section 5: Integers | Fractions |
1.5: Integers
In this section, we begin to expand beyond the scope of whole numbers by exploring negative numbers.

## Order and Absolute Value

The absolute value (or modulus) of a real number $a$, denoted by $|a|$ refers to its distance from zero on the real number line. This value is always taken to be nonnegative. For example, the illustration on the left shows the following:
$|-5|=5\ |3|=3$
The absolute value of -5 is 5 because it is 5 away from zero, and the absolute value of 3 is 3 because it is 3 away from zero. The absolute value of a positive number or zero is always itself. Conversely, the absolute value of a negative number is its opposite.
Likewise, the distance between two numbers on the number line can be thought of as the absolute value of the difference between them.
# Algebra/Contributors
## Completion Scale

* Sparse text 0-24%
* Developing text 25=49%
* Maturing text 50-74%
* Developed text 75-99%
* Comprehensive text 100%

## Extra

* To Do List
* Book Order
* Problem Bank
* Templates
# Chess Opening Theory/1. g3/1...h5
## Lasker Simul Special

interesting move. Black wants to advance the pawn to h4 to open the h-file.
Lasker Simul Special :
| | a | b | c | d | e | f | g | h | |
| 8 | | | | | | | | | 8 |
| 7 | | | | | | | | | 7 |
| 6 | | | | | | | | | 6 |
| 5 | | | | | | | | | 5 |
| 4 | | | | | | | | | 4 |
| 3 | | | | | | | | | 3 |
| 2 | | | | | | | | | 2 |
| 1 | | | | | | | | | 1 |
| | a | b | c | d | e | f | g | h | |
# Algebra/Multiplication Table

| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 |
| 13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 |
| 14 | 14 | 28 | 42 | 56 | 70 | 72 | 84 | 96 | 108 | 140 | 154 | 168 | 182 | 196 | 210 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 |
# Starting and Running a Wiki Website/Introduction

Since the inception of the World Wide Web and its general acceptance in the 1990s, internet engineers have exploited the capability of linkage to endeavor deeper into the semantic purposes of the web. Long gone are the days when the web was considered an alternative to other communication media. These days however, it is anything but. From music to video, richer multimedia content has revolutionized the power of links into something far superior than it was when it was designed.
Fueled by the collective intellect of people from all corners of the globe, the Internet is growing at an accelerated speed. Internet can no longer be called a technology, Internet is the people!
People brought together under the banner of a common interest, e.g., skiing, paragliding, etc., on the Internet form an online virtual community dubbed a web community. Trivial as it may sound, the notion of a community on the web has been the subject of many a books in the past decade and people have refrained from focusing more on the core technologies that build the web like HTML, JavaScript and CSS and rather thinking of ways of manipulating user interactions, interventions and interests to weave a social network.
This book in its concise form would give its readers a bird's eye view of the basics of developing such an online community, its pros and cons along with actual examples of work by others on the concept.

## What this book is about?

Community design fundamentals for the web - Throughout the book, we will be exploring different types of communities on the web and the very basic fundamentals they are racked upon. We will also look into a chronological evolution of design for such communities and peek into community building ideologies explored by virtual community pioneers and experts.
Tools and best practices - This book encourages the readers to focus on an array of best practices and tools for the creation of communities using key pointers from these very community researchers. Along the brick road, we may also focus on some of the many trends that are brewing towards a truly new breed of communities called Community 2.0.

## What this book is not about?

Not much technical babble involved - At some points, this book might even touch some technical aspects of community design albeit only where necessary. In its entirety, this book serves only as a text supplementing core concepts of community design and would not fall into deeper technicalities of it thereof. Advice on collection and usage of user-collected data may sometimes address some technical issues.
Building upon works and not just adoption - This book would be using existing web communities as a tool to teach robust design and in no way tends to limit readers into adopting similar concepts but rather advises them to use this text to think up original and creative experiences out of the box.

### See also

Next page: Overview
# Algebra/Chapter 2/Glossary

* angle:
* area:
* expression:
* perimeter:
* sentence:
* set:
# Algebra/Glossary
## A

* addition: The process of combining two numbers.

## D

* digit:
* division: The process of sharing an equal amount to a set group.

## E

* Expression: A mathematical sentence consisting of numbers, variables, and mathematical operators.

## I

* integer:

## M

* multiplication: The process of repeated addition.

## N

* number:
* number system:

## Q

* quantity:

## S

* subtraction: The process of taking away one number from another to find the difference between them.
# Glossary

* mathematics-
# Austrian Defence

The Austrian chess players Hans Haberditz (c. 1901–57), Hans Müller (1896–1971), and GM Ernst Grünfeld studied this defense, which was initially introduced by Italian chess player Alessandro Salvio in 1604. Black creates a lot of tension and aims to disrupt White's center and prevent white from seizing the initiative by mirroring White's moves, adding a little complexity to the position. This defence can be prone to equalizing quickly, if white doesn't know opening theory, but current theory suggests that white should gain a sizeable advantage with the appropriate moves.

### White's responses

White will probably reply with one of the following options:
* 3. cxd5 - The classical main line in the Austrian Defence.
* 3. dxc5 - Exchanging a central pawn for a flank pawn.
* 3. Nf3 - Inviting a transposition to the Tarrasch Defence.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 d5 2. c4 c5
| | 3 | 4 | 5 | 6 | Eval | Notes |
| Austrian Defence | cxd5 Qxd5 | Nf3 cxd4 | Nc3 Qa5 | Nxd4 Na6 | += | Main Line |
| Austrian Defence, Gusev Countergambit | ... Nf6 | e4 Nxe4 | dxc5 Qa5+ | Bd2 Nxd2 | +/− | |
| | ... ... | ... ... | ... Nxc5 | Nc3 e5 | +/− | |
| | ... ... | Nf3 cxd4 | Qxd4 Qxd5 | Nc3 Qxd4 | += | |
| Austrian Attack, Salvio Countergambit | dxc5 d4 | Nf3 Nc6 | e3 e5 | exd4 exd4 | += | |
| Tarrasch Defence, Psuedo-Tarrasch | Nf3 e6 | cxd5 exd5 | g3 Nc6 | Bg2 Nf6 | += | By Transposition |
| Queen's Gambit Accepted, Gunsberg Defence | ... dxc4 | d5 e6 | e4 exd5 | exd5 Bd6 | += | By Transposition |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
* 1 d4 d5 and Unusual Replies to the Queen's Gambit, Nunn, John (ed.), et al. (1999). Nunn's Chess Openings. Everyman Chess, ISBN 1-8574-4221-0.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Quantum Chemistry/Finding maxima
## The Process of finding a maximum of a function

The maximum of a function is found by first computing the derivative of the function $f'(x)$, as it describes the rate of change of the original function $f(x)$. At a maximum, the slope of the function changes from positive where the function is increasing to negative where the function is decreasing. Therefore, the slope is equal to zero at a maximum: $f'(x)=0$. The points at which $f'(x)=0$ are denoted as critical points. It is important to note that not all critical points are maximums since there are other instances where the slope is equal to zero, such as a minimum or inflection point of the function. To determine whether a critical point is a maximum, the second derivative of the function $f''(x)$, must be computed. It describes the concavity of the function and how its slope is changing. If $f''(x)<0$, the function is concave down and the critical point is a maximum.

## Example Problem
### Problem

Find the maximum of the function
$r^{2}\exp(-r^{2})$

### Solution

Determining the critical points
Compute the derivative $f'(r)$ of the function.
Since $r^{2}\exp(-r^{2})$ takes the form $f(r)\cdot g(r)$, it can be differentiated using the product rule.
    Product Rule ${\frac {d}{dr}}[f(r)\cdot g(r)]=f'(r)\cdot g(r)+g'(r)\cdot f(r)$ ${\frac {d}{dr}}[r^{2}\exp(-r^{2})]={\frac {d}{dr}}(r^{2})\exp(-r^{2})+(r^{2}){\frac {d}{dr}}\exp(-r^{2})$
$f'(r)=2r\exp(-r^{2})-2r^{3}\exp(-r^{2})$
$f'(r)=2r\exp(-r^{2})(1-r^{2})$
Since a maximum occurs when the slope is zero,
$2r\exp(-r^{2})(1-r^{2})=0$
The points at which the function equal zero are the critical points. Since $\exp(-r^{2})$ will never equal zero,
$2r=0$ when $r=0$
$1-r^{2}=0$ when $r=\pm 1$
Therefore, the critical points are $0,-1,1$
Evaluating the critical points
Compute the second derivative $f''(x)$ of the function.
Since $f'(r)=2r\exp(-r^{2})(1-r^{2})$ again takes the form $f(r)\cdot g(r)$,
${\frac {d}{dr}}[2r\exp(-r^{2})(1-r^{2})]={\frac {d}{dr}}(2r\exp(-r^{2}))(1-r^{2})+(2r\exp(-r^{2})){\frac {d}{dr}}(1-r^{2})$
$f''(r)=(2\exp(-r^{2})-4r^{2}\exp(-r^{2}))(1-r^{2})+(2r\exp(-r^{2}))(-2r)$
Evaluating $f''(r)$ at the critical points determines the concavity of the function.
When $f''(r)<0$, the critical point is a maximum.
At $r=0$, $f''(0)=2$.
At $r=1$, $f''(1)=-4\exp(-1)$
At $r=-1$, $f''(-1)=-4\exp(-1)$
Since $-4\exp(-1)<0$, the points $r=1,-1$ are maximums.
# Introduction to Programming Languages/Scoping with Namespaces

Namespaces are named program regions used to limit the scope of variables inside the program. They are used in many programming languages to create a separate region for a group of variables, functions, classes, etc. The usage of namespaces helps to avoid conflict with the existing definitions. Namespaces provide a way of implementing information hiding. Some examples of namespaces in Java are classes and packages. Examples of namespaces in C++ are classes, namespaces, and struct. The source code bellow illustrates the usage of namespace in Java:
The Java code above defines a namespace called geometry. This definition provides a way of discriminating the class Circle from others that could be defined by other programmers. This discrimination is performed because the defined namespace is incorporated to the class. So, the class becomes geometry.Circle. The first line of the code shows an import statement, which is the way Java shares definitions. It is interesting to note that the method getArea uses the definition pi from the imported namespace calc.math.
In C++ language, the namespace keyword is used to create namespaces. The include statement is a way of sharing definition in C++. The next example illustrates the definition of two namespaces (first and second) and their use. Namespaces are usable by taking their name reference with scope resolution operator (operator "::"). This is illustrated in the statement cout << first::var << endl; at line 14. Namespaces are also used with the using keyword, which makes all the members of the namespace available in the current program and the members can be used directly, without taking reference of the namespace. The statement present in the line 3 of the code makes the cout object available in the function main without the usage of the scope resolution operator.
The keywords private and public, which will be better detailed in other section of this wikibook, modify the visibility of the definitions in a namespace. There is no difference between a class and a struct in a C++ program, except that by default, the members of a struct are public, and the members of a class are private. Also structs are by default inherited publicly and classes by default are inherited privately. Other than that, whatever you can do in a class, you can do in a struct.
Language library is a collection of definitions and implementations that provide ready-to-use functions. They are a way to grow a programming language. In a C++ program, a library can be included using the #include directive. The previous C++ example used this construct in the line 1 to include the iostream library.
← Scoping with Blocks
# Special Relativity

The book is divided into two sections, an introductory text and a more advanced text. Both texts cover the same topics. Undergraduates might compare their curriculum with the text and study appropriately.

## Introductory text

This book is part of a series on Modern Physics:
Waves General Mechanics Special Relativity Quantum Mechanics Electrodynamics Nuclear Physics
Introduction
* Historical Development
Principle of Relativity
* The principle of relativity
* Frames of reference, events and transformations
* Special relativity
* The postulates of special relativity
Spacetime
* The modern approach to special relativity
* Spacetime
* The lightcone
* The Lorentz transformation equations
Simultaneity, time dilation and length contraction
* The relativity of simultaneity and the Andromeda paradox
* The nature of length contraction
* Evidence for length contraction, the field of an infinite straight current
* De Broglie waves
* The twin paradox
* The pole barn paradox
* Addition of velocities
Dynamics
* Introduction
* Momentum
* Force
* Mass and energy
Aether
* Introduction
* The aether drag hypothesis
* The Michelson-Morley experiment
* Mathematical analysis of the Michelson Morley Experiment
* Lorentz-Fitzgerald contraction hypothesis
Faster than light signals, causality and Special Relativity

## Advanced text

Mathematical transformations
* Introduction
* The Lorentz transformation
* The linearity and homogeneity of spacetime
* The Lorentz transformation
* Length contraction, time dilation and phase
* Hyperbolic geometry
* Addition of velocities
* Acceleration transformation
Waves
* Relativistic waves
* Principle of Relativity Applied
* Characteristics of Relativistic Waves
* The Doppler Effect
Relativistic dynamics
* Introduction
* Momentum
* Relativistic Mass
Mathematical approach
* Vectors
* Matrices
* Linear Transformations
* Indicial Notation
* Analysis of curved surfaces and transformations
* Four vectors
Problems

## Appendices

* Mathematics of the Lorentz Transformation Equations

## Further Information

* Modern Physics
* General Relativity