OpenLLM-France/wikimedia huggingface dataset:
# Basic Algebra/Systems of Linear Equations/Chapter Review

Lesson 1. Solving Linear Systems by Graphing
Lesson 2. Solving Linear Systems by Substitution
Lesson 3. Solving Linear Systems by Linear Combinations
Lesson 4. Using Matricies to Solve Linear Systems
# Basic Algebra/Solving Equations/Solving Equations with Multiplication and Division
## Vocabulary

Coefficient - A natural number (the numbers used for counting) next to a variable (the letter for which we solve the equation, also known as an unknown). For example, a variable with a coefficient of 3 would be 3x.

## Lesson

Like in the previous section, the goal is to isolate the Variable. In other words, get the variable on one side, and the constants on the other.
However, what happens when we are dealing with multiplication on a Variable?
if x is some number, 3x means three times that number.
In order to isolate the variable, we have to get rid of the coefficient. You can choose to do this before OR after you move the constants like you did in the previous section, although it's generally easier to do so afterwards.
Fractional coefficients are Basically just division. 1/2 of some number x can be written as (1/2)x or x/2. This can be helpful to remember, because all that you have to do in either case, all you have to do is multiply both sides by the bottom number, and presto chango, you have a solved equation.

## Practice Games

put links here to games that reinforce these skills

## Practice Problems

Use / as the fraction line and put spaces between the wholes and fractions!
# Basic Algebra/Solving Equations/Solving Equations with Variables on Both Sides of the Equation
## Vocabulary
### Variable

    A letter ($a$-$z$) that takes the place of a number.

### Equation

    An example would be like $8y-3=1+10y$ (The answer is $y=-2$ )

## Lesson

NOTE: WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER SIDE! NO EXCEPTIONS!
1) do the distributive property.
2) Combine like terms on both sides.
3) add/subtract numbers next to a variable on both sides.
4) divide by the number next to the variable on both sides.
5) The answer should look like: $x=20$ or $20=x$.
(Note: the variables and numbers may vary in your answer.)

## Example Problems

A simple problem:
| $2(x+5)=5(x-10)$ $2x+10=5x-50$ $2x+10-2x=5x-2x-50$ $10=3x-50$ $10+50=3x-50+50$ $60=3x$ $60/3=3x/3$ $20=x$ | Problem Distributive Prop. Subtract the variables with numbers next to them. This is what you're left with. get rid of the 50 by subtracting This is what you're left with. Get rid of the three by dividing by three This is your answer. |

## Practice Games

Put links here to games that reinforce these skills
Purplemath.com: http://www.purplemath.com/modules/index.htm

## Practice Problems

Note: Use / as the fraction line and put spaces between wholes and fractions!
# Basic Algebra/Solving Equations/Solving Multi-Step Equations
## Lesson

A multi-step equation is an equation that needs two or more steps to do. Our goal is to let the variable to be on its own on one side of the equal sign. You have to get rid of the numbers other than the variable on the side before the equal sign. If you do anything to a side you have to do the same thing on the other side. Solving multi-step equation is just like solving a one-step equation with more steps.

## Example Problems

Solve 4 x - 5 = 15
First we must get rid of the five by addition on both sides.
4 x - 5 = 15
4 x - 5 + 5 = 15 + 5
4 x = 20
Then divide four on both sides.
4 x = 20
4 x ÷ 4 = 20 ÷ 4
x = 5
We found our answer, x = 5
Solve 3 x + 6 = 27
First we must get rid of the 6 by subtraction on both sides.
3 x + 6 = 27
3 x + 6 - 6 = 27 - 6
3 x = 21
Then we have to divide by three on both sides.
3 x = 21
3 x ÷ 3 = 21 ÷ 3
x = 7
The Answer is, x = 7

## Practice Games

put links here to games that reinforce these skills
# Basic Algebra/Solving Quadratic Equations/The Zero Product Property
## Lesson

The zero property is based on the elementary concept that when you multiply two numbers and the answer is zero, then one of the numbers multiplied must be zero.
Rule: if a × b = 0, then a = 0 or b = 0.
Meaning that the zero property establishes that a or b has to equal zero in order for the result to be zero, a or b could be any random number while the other variable is zero so that result would still be zero.

## Example Problems

(x+5)(x-3)=0
x+5=0 x-3=0
x=-5 x=3

## Practice Problems

Easy
Medium
Hard
# Basic Algebra/Solving Quadratic Equations/Solving Quadratic Equations By Taking The Square Root of Both Sides
## Lesson

One way to solve a quadratic is to use square root. Steps:
* Factor a quadratic so that it is in the form $y=(x+z)^{2}$ ($z$ can be determined by completing the square)
* Take the square root of both sides, so $x+z=\pm {\sqrt {y}}$
* If y is 0, the square root is zero. In this case, there will only be one solution instead of two.
* Solve for x

## Example problems
### Problem 1

${\begin{aligned}200&=2x^{2}+38\\162&=2x^{2}\\81&=x^{2}\\x&=\pm 9\end{aligned}}$

### Problem 2

${\begin{aligned}64&=x^{2}+6x+9\\64&=(x+3)^{2}\\x+3&=\pm 8\\x&=-3\pm 8{\text{, i.e., }}x=\{-11,5\}\end{aligned}}$
# King's Indian Defence - Sämisch Variation
### 5. f3

5. f3 is the Sämisch Variation, a well-known and popular line in the King's Indian. With this solid move white bolsters his centre. He remains noncommittal with regards to his king, with castling both queenside or kingside possible depending on what black does. This can be a tough nut to crack for black, who usually wants white to overextend when playing the King's Indian.
However, the Sämisch does have some drawbacks for white. Most obviously, kingside development is impeded because the king's knight cannot go to its usual square, f3. Secondly, the g1-a7 diagonal is open and on a direct line to white's king, should white castle short. The Sämisch has fallen somewhat out of favour at the highest levels of chess for the more natural-looking 5. Nf3, but it's still sometimes seen in grandmaster play. At the amateur level, this variation remains perfectly viable and gives both sides good chances.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f3
| Sämisch Variation | ... O-O | Be3 Nc6 | Qd2 a6 | Nge2 Rb8 | = |
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## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# King's Indian Defence
### 5. ... O-O

This is the standard line. Black castles and prepares to exploit his lead in development.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f3 O-O
* 6
* Be3
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# Chess Opening Theory/1. d4/1...Nf6/2. c4/2...g6/3. Nc3/3...d5/4. cxd5/4...Nxd5/5. e4
## 5.e4

This move greedily grabs central space. Since Nf6 or Nb6 would leave black without enough pressure in the center, Nb4 misplaces the knight only to create the obvious threat of Qxd4 followed by Nc2, Nxc3 is forced. Although d4 is strengthened, the queenside weakens, and the a1-h8 diagonal loosens up. That is why g6 and Bg7 is played in the Gruenfeld Defence. Black will now play to dismantle white's central ambitions. Usually, Black advances the c-pawn, and then he uses his e-pawn to dismantle white's center. Also, Nb4?? loses to Qa4+ Nc6 d5.
After e4, White has a dangerous center. Black must pressure it or risk a cramped, passive game. The only good move is Nxc3, else play resembles the dubious Marshall defence.

## Theory table

| 5 | 6 | 7 | |
| e4 Nxc3 | bxc3 Bg7 | Nf3 c5 | = |
# King's Indian Defence
### 6. Be3

White defends the d4 pawn, which is usually the weakest in the Sämisch formation. Black now has a variety of options - usually he wants to strike in the centre with ...e5 or even the gambit line ...c5. The latter, although it gives up a pawn, gives black a lead in development with plenty of open lines and white's extra pawn is doubled, limiting its usefulness. In practice, black scores very well with the gambit line and it is partially due to it that the Sämisch is not quite as popular as it once was.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f3 O-O
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
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# Grünfeld Defence - Exchange Variation

White captures the lone central black pawn and forces Nxd5, after which White can create a huge center with e4.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3.Nc3 d5 4.cxd5
| 4 | 5 | 6 | 7 | 8 |
| cxd5 Nxd5 | e4 Nxc3 | bxc3 Bg7 | Bc4 O-O | Ne2 Nc6 | +/= |
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## References

de Firmian, Nick. Modern Chess Openings, 15th Edition. New York, NY: Random House, 2008.
# Grünfeld Defence - Exchange Variation
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3.Nc3 d5 4.cxd5 Nxd5
| 5 | 6 | 7 | 8 |
| e4 Nxc3 | bxc3 Bg7 | Nf3 c5 | Rb1 O-O | ∞ |
| Na4 Bg7 | e4 Nb6 | Be3 O-O | Nf3 Bg4 | = |
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## References

* Modern Chess Openings: MCO-14. 1999. Nick de Firmian, Walter Korn. ISBN 0-8129-3084-3.
# Chess Opening Theory/1. d4/1...Nf6/2. c4/2...g6/3. Nc3/3...Bg7/4. e4/4...d6/5. Nf3/5...O-O/6. Be2/6...e5
## 6. e5

The move e5 from Black attacks the center and gains space. The main line continues by White castling kingside to get the king away from the center, then Black plays Nc6 to gain space and develop a piece, which White immediately kicks with d5, forcing it to e7. From there, the game can branch off in several different ways.
b4 makes a pawn storm on the queenside, with the rooks developing to support in the attack. In some games, Black's kingside knight goes to h5 then back to f6 on its own volition to push the f-pawn to f5 to destabilize the center and prepare g4.
Ne1 eventually rotates the knight to the center after Nd3 where it can defend better against Black's counterattack, be protected from g4as well as attack in the future. Black's kingside knight also moves to allow f5.

## Theory Table

1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. Nf3 O-O 6. Be2 e5
| 7 | 8 | 9 | 10 |
| O-O Nc6 | d5 Ne7 | Ne1 Nd7 | Be3 f5 | +/= |
| ... ... | ... Nd4 | Nxd4 exd4 | Qxd4 Nd7 | +/= |
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# King's Indian Defence
### 5. f4

The Four Pawns Attack is the most aggressive line for White in the King's Indian. White creates a massive pawn centre and has full control over the middle of the board ... for now. This is a dangerous line for Black, and if they don't play correctly, they will be knocked off the board by White's advancing army. However, if Black can survive the initial onslaught, they will have the better game since White will have many weak squares in their camp that their pawns can't defend. For this reason, the Four Pawns Attack isn't seen frequently at the highest levels of chess, although it's still very viable at the amateur level.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f4
| Four Pawns Attack | ... O-O | Nf3 c5 | d5 e6 | Be2 exd5 | =∞ |
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## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Grünfeld Defence

This is the classic starting position of the Grünfeld Defence, although d5 can be delayed if White has delayed e4 which typically happens if Nf3 is played at some stage.
Black plays d5 and challenges White's occupation of the center. White has a range of choices, the main one is to exchange the pawns on d5 to displace Black's pieces.
During the 1920s, European chess was in revolution, with the entry of the Nimzo-Indian Defence into mainstream opening theory. The masters of the day termed this the "Modern style". Then, in 1922, a well-known master named Ernst Grünfeld came up with a new system that started bashing the great masters of the day, including Alekhine, Kostic, Sämisch, and Colle. This came to be known as the new "hypermodern" style, and Grünfeld, true to hypermodern tastes, showed in pure form how the previously accepted classical dogma could be wrong, and that a pawn center could be an object of attack as well as a boon.
The main battleground of philosophies is the Exchange Variation, 4.cxd5 Nxd5 5.e4 Nxc3 6.bxc3. White's pawn center gains space, but Black has excellent play along the long, dark diagonal from a1 to h8, and can eventually target d4 with moves like ...Bg7, ...Rd8, ...c5, ...Nc6, and occasionally ...Qa5. Eventually he may also bring a bishop to fianchetto on the other diagonal, targeting e4.
The more classical moves are 4.Nf3, 4.Bf4, and 4.Qb3, which are more conservative ways to fight Black's system. The pawn center still remains, but Black's counterplay is still adequate. The most positional move is 4.Bg5.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3.Nc3 d5
| | 4 | 5 | 6 | 7 | 8 |
| Exchange Variation | cxd5 Nxd5 | e4 Nxc3 | bxc3 Bg7 | Bc4 O-O | Ne2 Nc6 | +/= |
| Nadanian Variation | cxd5 Nxd5 | Na4 Bg7 | e4 Nb6 | Be3 O-O | Nf3 Bg4 | = |
| Brinckmann Attack | Bf4 Bg7 | e3 c5 | dxc5 Qa5 | Rc1 Ne4 | cxd5 Nxc3 | +/= |
| Russian System | Nf3 Bg7 | Qb3 dxc4 | Qxc4 O-O | e4 Nc6 | Be2 Bg4 | = |
| Stockholm Variation | Bg5 Ne4 | Bh4 Nxc3 | bxc3 dxc4 | e3 Be6 | Qb1 b6 | = |
| Lutikov Variation | f3 Bg7 | e4 dxe4 | fxe4 c5 | e5 Nh5 | +/= |
| Schlechter Variation, Makogonov Variation | e3 Bg7 | =/= |
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## References

de Firmian, Nick. Modern Chess Openings, 15th Edition. New York, NY: Random House, 2008.
# Grünfeld Defence - Nadanian Variation
## 5. Na4!?

This strange looking move was first employed by Ashot Nadanian in 1996. Usually it is not recommended to put Knights on the edge of the board, but here it is meaningful. White takes the important c5-square under control and going to force black's Knight from the center with е4. Eventually, the a4-Knight can occupy the c5-square and attack the pawn on b7.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. c4 g6 3.Nc3 d5 4.cxd5 Nxd5
| 5 | 6 | 7 | 8 | 9 | 10 |
| Na4 Bg7 | e4 Nb6 | Be3 O-O | Nf3 Bg4 | = |
| ... e5 | dxe5 Bb4+ | Bd2 Ne3 | fxe3 Bxd2+ | Qxd2 Qh4+ | g3 Qxa4 | ∞ |
| ... Nf6 | Nf3 Bg7 | g3 Nc6 | Bf4 Nd5 | ∞ |
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## References

* Modern Chess Openings: MCO-14. 1999. Nick de Firmian, Walter Korn. ISBN 0-8129-3084-3.
* Nunn's Chess Openings. 1999. John Nunn (Editor), Graham Burgess, John Emms, Joe Gallagher. ISBN 1-8574-4221-0.
# An Introduction to Civilizations/About Civilizations

Civilizations have been very important to the evolution of human history. For example the Sumerians invented the wheel. Even though this was a very ancient invention our modern "gadgets" such as car depend on wheels. Also these ancient civilizations are the basis of some of our traditions. For example Halloween was the day the Ancient Celtics thought that the ghosts and spirits would come out. Today we all dress up as ghosts and spirits. And as for languages. Our alphabets are mainly based on ancient symbols. And our words are based on ancient roots. All in all, The ancient peoples of the world played a very important role for our society.

## Sumer the first civilization

The first society known to date was Sumer. Sumer was an ancient civilizations that was very modernized for their time. The Sumerians invented the wheel. That invention changed transportation on Earth forever. The Sumerians also invented the earliest form of writing. This form of writing was called Cuneiform. Cuneiform was based on symbols and hieroglyphics. The last thing Sumerians did was they invented boats. They invented boats from the reeds off the river bank. This was because the Sumerians also were the first people to trade among each other. The Sumerians in many different way shaped all of Earth's societies and civilizations.
# Blender 3D: Noob to Pro/Softbodies

Next page: Paths Previous page: Intermediate Animation
A quick softbody tutorial just to demonstrate the new system. Needs some work.
The softbody system in Blender makes each edge of your object behave like a spring, and gives each vertex a weight. It is thus a very effective way to simulate physics. The easiest (and coolest :) way to explain it is to give a demonstration.
We'll make a donut shape, and then make it springy and let it drop onto a plane.
Donut shape: Ctrl-x for a new blender file if you haven't already. Be sure to delete the default cube, you won't be needing it. Goto the front view and add a circle with 8 vertices. Move the circle 5 squares to the right (holding down ctrl). Top view, press F9, and in the Mesh Tools window (in editmode) set Degr to 360, Steps to 8 and Turns to 1, make sure the 3D cursor is at the origin, and hit Spin. Select all vertices, and hit Rem Doubles. Turn on Subsurf, (which I won't bother mentioning is a modifier, found in the modifiers/shapes panel, inside the editing window) and set it to 2 iterations. We have achieved donut.
Add a plane (as a separate object) under the donut, and scale it up so that the donut has something to fall on to. It should be about 3 grid units under the donut. Press F7 and find the Particle tab, then turn on Deflection. This will make our donut bounce off the plane.
Select the donut again. Press F7 and find the Softbody tab. Hit Enable SoftBody and set Grav to 9.8 (this puts a downward force on each vertex). Turn off Use Goal (Goals are used to give each vertex a (partly) predefined position, and are too complicated for this tutorial) and turn on Stiff Quads. Hit Alt-A to animate... amazing! :)
Now some fiddling with the settings... Put E Stiff up to 0.9 to get a nice jelly effect. Alt-A again. With some objects (e.g., spheres, cylinders), if E Stiff is too low the object will collapse. This can be remedied by putting edges inside the object (i.e. through the volume) to help them keep their shape. Stiff Quads means that quads (the four-sided faces) get diagonal springs to help keep them in shape too... (insert joke about quads and working out here :).
There is huge potential in the softbody system. Try rotating the donut and the plane to get the donut to roll along the plane :) Things tend to roll better if softbody damping on the Deflection tab is turned up high.
To see a collapsing object, use a cylinder instead of a donut.
As of version 2.37a, Blender has no support for softbodies colliding into other softbodies.
Note also that the normal of the plane must be pointing towards the donut.
Next page: Paths Previous page: Intermediate Animation
# Sicilian-Rossolimo Variation

3. Bb5

## Theory table

1.e4 c5 2.Nf3 Nc6 3.Bb5
| | 3 | 4 | 5 | 6 |
| | Bb5 g6 | O-O Bg7 | c3 Nf6 | Re1 O-O | = |
| | ... e6 | O-O Nge7 | Nc3 a6 | Bxc6 Nxc6 | += |
| | ... d6 | O-O Bd7 | Re1 Nf6 | c3 a6 | += |
| Nyezhmetdinov-Rossolimo Attack | ... Nf6 | Nc3 a6 | Bxc6 dxc6 | e5 Ng4 | h3 Nh6 | d3 Nf5 | Ne4 e6 | c3 b5 | g4 Nh4 | Bg5 Be7 | += |
| | ... Nf6 | Nc3 Nd4 | e5 Nxb5 | Nxb5 Nd5 | += |
| | ... a6 | Bxc6 dxc6 | | | +/= |
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## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Portsmouth Gambit

A variant of the Wing gambit. White sacrifices the b4-pawn for a semi-open b-file and sometimes an open c-file, along with control of the center and quick development. This also frees up the a1–h8 diagonal. If Black declines the gambit, White has the threat of bxc5, or even sometimes b5.
In contrast to the regular Wing gambit, after 3...cxb4, White will play 4. d4. In many positions d5 is a threat, forcing the knight to either go to a5 or back to b8.
If Black captures with the knight, White will attack it with 4. c3. After 4...Nc6, White will attack the center with 5. d4.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. e4 c5 2. Nf3 Nc6 3. b4
| 4 | 5 | 6 | 7 |
| ... cxb4 | d4 d5 | exd5 Qxd5 | c4 bxc4 | = |
| ... Nxb4 | c3 Nc6 | d4 cxd4 | cxd4 e6 | ⩱ |
| ... e5 | b5 Nd4 | Nxe5 Qe7 | Nc4 Qxe4+ | = |
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# Sicilian, Taimanov
### 3...e6
## Theory table

1.e4 c5 2.Nf3 Nc6 3.Nc3 e6
| | 4 | 5 |
| Sicilian, Taimanov | d4 cxd4 | |
| | Bb5 Nge7 | |
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* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Chess Opening Theory/1. e4/1...c5/2. Nf3/2...Nc6/3. Bb5/3...a6
## 3...a6?!

This move attacks the bishop but since White wanted to trade it off anyway, this effectively wastes a move.
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# Sicilian, Rossolimo Variation
### 3...g6
## Theory table

1.e4 c5 2.Nf3 Nc6 3.Bb5 g6
| | 4 | 5 |
| Sicilian, Rossolimo Variation | O-O Bg7 | |
| Sicilian, Rossolimo Variation | Bxc6 dxc6 | |
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# Chess Opening Theory/1. e4/1...c5/2. Nf3/2...Nc6/3. Nc3/3...d6
## 3...d6

This is the main line and is a non-committal move. Black retains flexibility to wait and see if white opens up the game with d4 or opts to keep it closed such as d3 and maybe c3 to prepare the hallmark d4 push and locking up the center.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1.e4 c5 2.Nf3 Nc6 3.Nc3 d6
| 4 | 5 | 6 | 7 |
| d4 | |
| Bb5 | |
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* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Chess Opening Theory/1. e4/1...c5/2. Nf3/2...Nc6/3. b4/3...cxb4

Black captures the b4 pawn, deflecting it from the defence of d4. White will now play d4.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. e4 c5 2. Nf3 Nc6 3. b4
| 4 | 5 | 6 | 7 |
| d4 d5 | exd5 Qxd5 | c4 bxc4 | Nxc3 Qa5 | = |
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