OpenLLM-France/wikimedia huggingface dataset:
# 0 A.D./Birth of 0 A.D.

The concept behind 0 A.D. has actually been in the works since the year 2000. It started out as a collaboration between several groups advocating several different ideas.
The first idea was a fan request put together by a gamers’ group called Tonto Clan. They compiled a game design for a remake of Age of Empires: The Rise of Rome, and intended to send it to Age of Empires developers Ensemble Studios and suggest that they implement it. This fell through because ES had a different concept in mind, which was to develop a game based on mythology rather than history. This game is now known as Age of Mythology.
Second, Wildfire Games’ predecessor, a modding team named Wildfire Studios, had completed a successful, large-scale mod for Age of Empires II: The Age of Kings (AoK) named “Rome at War”. Seeking to expand their success, they had started developing another mod at a much larger scale, changing many more art assets — a “total conversion” mod. While developing the mod, the team constantly ran into the limitations of modding a closed-source, proprietary game, and found that they could not change some features of the AoK engine, leading them to look into developing a standalone game.
Last but not least, a fantasy modding project, later called The Last Alliance (TLA), began looking into creating their own mod, and was also interested in the prospect of creating a standalone game with its own engine.
While at first, these three groups interacted independently on the forums of Age of Kings Heaven, an AoK fansite, they unified their ideas into the concept of a freeware, independent game engine to support 0 A.D. and TLA in the winter of 2001/2002. Jason “Wijitmaker” Bishop, a 23-year-old from Edwall, Washington, took the lead and would continue to manage the project for the next 6 years or so.
# 0.999.../The geometric series formula

    $\sum _{n=0}^{\infty }x^{n}=1+x+x^{2}+x^{3}+...$ is known as a geometric series.
If, $|x|<1$, then this series converges to:
    $\sum _{n=0}^{\infty }x^{n}={\frac {1}{1-x}}$
Proof: Define the partial sum $S_{n}$:
    $S_{n}=\sum _{n=0}^{n}=1+x+x^{2}+x^{3}+...x^{n-1}$
    $xS_{n}=\sum _{n=0}^{n}=..+x+x^{2}+x^{3}+...x^{n-1}+x^{n}$
Note that both partial sums have n terms. When they are subtracted only the first term in and the last term in $xS_{n}$ will remain:
    $S_{n}-xS_{n}=1-x^{n}$, which can be easily solved for $S_{n}$
Note that we have failed to establish when the infinite series converges. This requires an understanding of the what happens when we take the limit of the partial sum as n goes to infinity. This is left to the reader as problem 1.
Sample problems:
* Prove that sequence of partial sums, $\{S_{n}\}_{n=1}^{\infty }=\{S_{1},S_{2},S_{3},...\}$, converges if $|x|<1$.
* This can be used to convert other repeating decimals into fractions. For pedagogical purposes, it is better to begin with a known fraction. From such a list, we consider: 0.181818... . Convert this into a rational fraction.

## Footnotes

* See also Calculus/Sequences and Series/Exercises
* ↑ It is your duty to improve Wikibooks. Please write up your solutions and post them here ASAP.
* ↑ Note the two ways to write this sequence, the latter resembles set-theory notation, except that the order in which elements appear is important. See wikiversity:Set theory#Basic concepts and notation
* ↑ See for example http://www.factmonster.com/ipka/A0876707.html
# 0 A.D.

The 0 A.D. Book
This book is about 0 A.D., a free, open-source, historical Real Time Strategy (RTS) game currently under development by Wildfire Games, a global group of volunteer game developers. The game stands out as one of the longest-running open source games, and throughout its history has received numerous awards and brought together a solid community of contributors, including designers, programmers and musicians. In this way, throughout the chapters of this book, you can learn about not only the characteristics of the game but also a little of the history of its development, its technical challenges, and efforts to be faithful to the historical aspects, as the game puts a strong emphasis on historical accuracy.

## Game History

* Birth of 0 A.D. (2000-2002)
* Closed-Source Development (2003-2009)
* Open Source Release (July 2009)
* Adding factions (2009-2015)
* Changing teams (2016-2019)

## Matching History

* Time range
* Factions
* Maps
* Soundtrack

## Technical Challenges

* Pyrogenesis
* Pathfinder
* Petra AI

## Mods

* Delenda Est
* Millennium A.D.
* Ponies Ascendant
* Terra Magna

## Community

* Wildfire Games
* Artists
* Developers
* Musicians

## Future perspectives

* Educational uses

## Attachments

* Releases

## Read More

* The Pyrogenesis Engine
# 0.999.../Proof from 0.333...
## Assumptions

* Decimal long division
* Decimal multiplication by a small number

## Proof

Using long division,
${\frac {1}{3}}=0.333...$
Multiplying both sides by 3, we have
${\frac {3}{3}}=0.999...$
and therefore...
$1=0.999...$
# 0.999.../Proof from 0.111...
## Assumptions

* Decimal long division
* Decimal multiplication by a small number

## Proof

Using long division, $^1$⁄$_9$ = 0.111…. Multiplying both sides by 9, we have 1 = 9 × 0.111… = 0.999…. Furthermore, because $^x$/$_x$=1, $^9$/$_9$=1. However, $^1$/$_9$=0.111..., so multiplying the numerator by nine, and thereby multiplying the answer by nine, produces 0.999... in terms of decimals, but, in terms of fractions, a numerator that is equal to the denominator.
# 0.999.../The limit of a sequence

In calculus, sequences such as a$_1$=1/1, a$_2$=1/2, a$_3$=1/3..... are discussed. However, most mathematicians and the majority of the mathematical laity prefer the notation a$_n$=1/n (n≥1) for the sequence above. Often, the limit of a sequence is discussed. A sequence a is said to converge to a limit L if a becomes arbitrarily close to L and stays there. For the case of 0.9999..., the sequence would be a$_n$=1-10$^{-n}$, where n is the number of 9's after the decimal point. For infinitely continuing digits, as n→∞, a$_n$=1-10$^{-∞}$, thus proving that 0.999999999... until infinity tends to 1.
# 0 A.D./Changing teams
## Passing the Torch

At the end of 2016, Johansson passed on the torch of project leader to Nicolas (“Itms”) Auvray, a Physics student from France in his early 20’s. Johansson continues to be the Administrative Head of Wildfire Games, thus continuing a sustained involvement of more than ten years in the project.

## Current State

0 A.D. is over 15 years in development and still not done, but it has come a long way and continues to make substantial improvements. Missing features are less and less numerous, and the community of players and contributors is thriving. The time and effort contributors have put in is comparable to what goes into developing a regular AAA title, and those can take up to 7 years to create, even with a greater and steadier input of work. Open source game projects of this scale lasting for this long is truly a rare, yet positive, occurrence.
# 0.999.../Proof by the geometric series formula
## Assumptions

* Definition from series
* The geometric series formula

## Proof

Using the series definition of the value of an infinite decimal,
    $0.999\ldots =9\left({\tfrac {1}{10}}\right)+9\left({\tfrac {1}{10}}\right)^{2}+9\left({\tfrac {1}{10}}\right)^{3}+\cdots .\,$
This is a geometric series with a common ratio of 1/10. Applying the geometric series formula,
    $0.999\ldots =9\left({\tfrac {1}{10}}\right)+9\left({\tfrac {1}{10}}\right)^{2}+9\left({\tfrac {1}{10}}\right)^{3}+\cdots ={\frac {9\left({\tfrac {1}{10}}\right)}{1-{\tfrac {1}{10}}}}=1.\,$

## Notes

Recall that,
    $\sum _{n=0}^{\infty }ax^{n}=\lim _{t\to \infty }{\frac {a(1-x^{t})}{1-x}}\underbrace {=} _{{\text{Given }}|x|<1}{\frac {a}{1-x}}$
# A Beginner's Arduino Guide/Projects/Controlling a motor's speed

In this page you will use an Arduino board to control the speed of a brushed motor.
# A Beginner's Arduino Guide/Where to get Arduino

There are several types of Arduino controllers:

## Genuine Arduino Controllers

These controllers usually cost about $25 USD. Most of the funding goes to support the Arduino organization. We strongly encourage you to purchase at least one Genuine Arduino or make a contribution to the project.
Genuine controllers often work best with the Arduino software. They use common serial controller chips such as the FTDI chip that have certified signed drivers for both the PC and Mac.

## Arduino Compatibles

Arduino compatibles are distinct from clones, in that they usually have distinct capabilities and significantly different hardware from official Arduino models. Arduino compatibles typically have their own branding, and don't try to pass themselves off as official Arduinos.
Here are some common features compatibles add or change compared to official Arduinos:
* Different microcontroller (More power efficient, more powerful, different architecture, etc)
* Different USB or serial port.
* Solderless expansion connectors.
* Built in Wireless radio for Wi-Fi, Bluetooth, etc.
* Built in sensors.
* Different formfactors.

## Arduino Clones

Because Arduino is open source, there are a number of Arduino clones that simply use official designs with either no modification, or modifications exclusively for cost reductions. These clones are typically unbranded, though less scrupulous sellers may try to pass off counterfeits falsely labeled as official Arduino boards.
These are typically around $5, however you can find some Arduino Nano versions for as little as $2.27 (includes shipping). eBay is a popular place to purchase Arduino controllers, however be warned that many of the suppliers are in Hong Kong and China, and shipping times can be longer then usual. Allow one or two weeks for shipping at a minimum. Don't be shocked if a clone unit is a dud or acts funky - it comes with the territory.
The lower-cost Arduino Clones use a lower-cost serial interface chip such as the CH340D. The drivers for these chips are not included in the Arduino IDE. You must install these drivers manually.
# A Beginner's Guide to D/Before We Begin.../D Compiler

There are currently three versions of the D compiler available. Digital Mars provides the DMD compiler, while there is a front end for the GNU Compiler Collection available called GDC, and a front end for the LLVM compiler called ldc.
The DMD compiler supports Windows, Linux x86, and OS X, whereas GDC and LLVM support many more platforms.
At the time of writing, the homepage boasts support for:
* Linux (tested on Fedora Core 5 x86 and PowerPC)
* Mac OS X 10.3.x, 10.4.x, 10.5.x
* FreeBSD 5.2.1
* Cygwin
* MinGW
* AIX (tested on 5.1)
On January 2, 2007, DMD released version 1.0 of their compiler, and GDC released version 0.21, which is based on the specification for DMD 1.0.
On January 9, 2009, the ldc project released a D frontend for the LLVM compiler. It supports OS X, Windows and Linux.
On February 11, 2009, DMD released dmd 1.040 (GM) binaries for OS X 10.5, Windows x86 and Linux x86.
On February 14, 2009, DMD released dmd 2.025 (alpha) binaries for OS X 10.5, Windows x86 and Linux x86.
# A Beginner's Arduino Guide/Projects/Digital Display

There are several kinds of displays that can be used with an Arduino.
* Character based - Typically easy to work with, these are usually designed to output text only.
* Graphical - More difficult to work with. Allows the display to draw arbitrary images.
# A Beginner's Arduino Guide/Projects/Sensors

You can make use of sensors to detect events and changes in the real world, and have your Arduino respond to them.
Common sensors include:
* Photosensors - Measures the level of light in an area.
* Microphones - Often used for detecting loud noises. (Most Arduino computers aren't suitable for voice recognition)
* Ultrasonic rangefinders - Bounces inaudible sounds off of objects and listens for their echo to determine distance from objects.
# A Beginner's Guide to D/Before We Begin...

* Short Introduction to D
* D Compiler
* Editors Supporting D
# A Beginner's Arduino Guide/Projects/Getting the LED to flash

In this chapter, you will learn how to get the LED to flash on an Arduino board. This is one of the simplest projects that you can undertake.
# A Beginner's Arduino Guide/Projects/Measuring a voltage

In this chapter you will use an Arduino board to measure the voltage of a battery.
# AQA A-Level Physics/Scalars and vectors

The term "scalar" means either that a quantity has no direction or to refer to such a quantity, whereas the term "vector" refers to a physical quantity or interaction that possesses both magnitude and direction.
Examples of scalars include:
* Temperature
* Energy
* Distance
* Speed
* Mass
* Charge
By contrast, the following quantities are vector quantities:
* Velocity (This is the distinction between speed and velocity, hence why a negative velocity is possible but not a negative speed)
* Displacement (Vectored distance)
* Momentum (Equal to mass multiplied by velocity; a vector multiplied by a scalar remains a vector)
* Impulse (Change in momentum)
* Force (Not a physical quantity, but force remains an essential point in mechanics. Note that F = ma shows that force is a vector in the same way that p = mv or I = Δp does)
* Acceleration
Vector quantities are typically represented by arrows in the correct direction on forces diagrams. Note that the type of arrow differs by the quantity in question. For example, acceleration is typically illustrated by way of an arrow with two non-filled heads along the body (e.g. ->->- 5ms $^{-2}$ )
Two vectors quantities may be added if they are representative of/act upon the same body; this is usually done using a scale diagram.
A single vector may be broken up into a number of perpendicular parts equal to the number of dimensions in which it is acting. For example, a force of (√2) Newtons that acts at an angle of 45$^0$ to the horizontal may be split into a force of 1N acting vertically upwards and a force of 1N acting horizontally.
# AQA A-Level Physics/Simple Harmonic Motion

Simple Harmonic Motion- Objects can oscillate in all sorts of ways but a really important form of oscillations is SHM or Simple Harmonic Motion. An object is undergoing SHM if:
* The acceleration of the object is directly proportional to its displacement from its equilibrium position.
* The acceleration is always directed towards the equilibrium position.
The frequency of an oscillation is measured in Hertz, and is the number of oscillations per second. The time for one oscillation is known as the period (T) and is measured in seconds.
Acceleration: we can calculate the acceleration of the object at any point in its oscillation by using this equation.
In this equation; a is the acceleration, f is the frequency in Hertz and x is displacement from the central position in metres.
Displacement: (When using this equation in the calculator, make sure that it’s in radians) You can calculate the displacement of the object at any point in its oscillation using this equation.
The terms of this equation are the same as that of acceleration. The extra terms in the equation are A which is the amplitude (or maximum displacement) in metres, t the time since the oscillation began in seconds.
Velocity: We can calculate the velocity of the object at any point in its oscillation using the equation below
The terms in this equation are the same as the equations above. The extra term in this equation is v, which funnily enough is the velocity.
SHM graphs:
These graphs show displacement, velocity and acceleration respectively. These graphs show how displacement and acceleration are proportional but in opposite directions, and also how when you have the minimum displacement, velocity is at its maximum. These are important notions to remember as they’re specific to SHM and allow us to determine whether an object or system does in-fact move with SHM.
The velocity equation simplifies to the equation below when trying to find the maximum speed (which will be at the point of minimum displacement)
The acceleration equation simplifies to the equation below when we just want to know the maximum acceleration (which is at the point of maximum displacement e.g why it uses the Amplitude of the system)
SHM and Energy: For a pendulum undergoing SHM energy is being transferred back and forth between kinetic energy and potential energy. The total energy remains the same and is equal to the kinetic energy + potential energy at any point within the motion.
# AQA A-Level Physics/Particles and Anti-particles/Particle-Antiparticle interactions

A high-energy photon may, under certain circumstances, produce a particle-antiparticle pair through the process of 'pair production'. On the other hand, one particle and one antiparticle, should they come into contact with each other, annihilate to give out 2 photons (i.e. a pair of electromagnetic waves) through the process of 'annihilation'.
These two processes are the essential parts of particle physics, both following the equation for mass-energy conversion first proposed by Albert Einstein, E = mc^2.
For instance, in the annihilation process of one pair of electrons and positrons, the energy created by the pair is $E=2m_e c^2$, as all mass should be conserved by being converted into energy. In the production, the frequency required for the photon to create the pair can be calculated using E = hf = 2m_e c^2.
The most common form of pair production is electron-positron production. This is because they have a smaller mass than most other particles, and thus require less energy to create. For the sake of comparison, an electron has a rest energy of 0.510999 MeV (or 8.18 x10^-14 J), meaning that a photon needs a frequency of 2.468 x10^20 Hz to create an electron-positron pair, as opposed to the proton's rest energy of 938.257 MeV (1.50x10^-10 J) and accompanying frequency of 4.53 x10^23 Hz.
# AQA A-Level Physics/Past paper questions
## Atomic Structure

1) Give the number of nucleons and the number of electrons in an atom of $^{22}$Na. (2 marks)
Nucleons =
Electrons =
2) What is meant by the term isotope?
3) Define the following (3 marks)
When removed from an atom, forms a charge
Has the largest mass-charge ratio
When removed from an atom, lowers overall mass
# AQA A-Level Physics/Quarks and sub-atomic particles

At GCSE you would have learned about the subatomic particles known as protons and neutrons and electrons. However there are many more subatomic particles than this that can be divided into two groups, Hadrons and Leptons.
Hadrons
− Hadrons are particles that interact using the strong nuclear force. Hadrons come in two further groups, Baryons and Mesons.
Baryons are hadrons that can decay into or are protons. These include: protons, neutrons, antiprotons and antineutrons. Mesons are hadrons that do not decay into protons, such as: pions and kaons. Pions and kaons can be positive, neutral and negative.
Baryons and mesons aren't fundamental particles and so can be split into smaller particles known as quarks.
Leptons
− Leptons are particles that interact using the weak nuclear force. Leptons are fundamental particles and so can not be split into any smaller particles. These include: electrons, muons, electron neutrino, muon neutrino, and their respective antiparticles.
Quarks Quarks are the particles that make up Hadrons. All quarks have a charge. There are: up, down, strange, anti up, anti down and anti strange quarks. When Kaons decayed, scientists observed that the particle took longer to decay than predicted, meaning that the particle decayed under weak interactions. To explain this, they were given a property known as strangeness, which is exhibited by strange quarks (strangeness -1) and anti strange quarks (strangeness +1).
| | Up | Down | Strange | Anti Up | Anti Down | Anti Strange |
| Charge (C) | +2/3 | -1/3 | -1/3 | -2/3 | +1/3 | +1/3 |
| Strangeness (S) | 0 | 0 | -1 | 0 | 0 | +1 |
Baryons are made up of three quarks. The proton is made from uud quarks (charge +2/3 +2/3 -1/3 = 1), and the neutron is made from udd quarks (charge +2/3 -1/3 -1/3 = 0). Anti protons are made from anti up anti up anti down quarks, Anti neutons are made from anti up anti down anti down.
Mesons are made from 2 quarks, and always a quark and an anti quark.
# AQA A-Level Physics/Radioactive decay

Radioactive decay is when an unstable nucleus decays in a random manner.
In theory, there is no end to the life of a radioactive substance (the time it takes before the activity reaches zero)therefore the quantity used for dealing with the life of radioactive substances is the half life. Half life is defined as the time taken for the activity of the sample to halve. The half life remains the same throughout the life of the sample. Each type of element has a distinct half life, $t_{\frac {1}{2}}$. As the activity of the sample is proportional to the number of radioactive nuclides present the half time can also be calculated by the time taken for half of the radioactive nuclides in the sample to decay.
If you plot a graph of the natural logarithm of N (the number of radioactive nuclides) against time you will see that there is a linear relationship between the two. The steeper the gradient the more quickly the substance will decay which means it has a shorter half life. Half life is proportional to ${\frac {1}{\lambda }}$

# Equations

${\frac {\Delta N}{\Delta t}}=-\lambda N$
$N=N_{0}e^{-\lambda t}$
$t_{\frac {1}{2}}={\frac {ln2}{\lambda }}$
$A=\lambda N$

# Derivations of equations

Note - given that all equations above are provided in the AQA Formula booklet (which is provided in the exam), it is not necessary to memorise all of the equations, but it is a good idea to learn what the different symbols stand for.

## Deriving $N=N_{0}e^{-\lambda t}$

We can use this differential equation to derive an equation for N.
${\frac {dN}{dt}}=-\lambda N$
Separating and integrating:
$\int {\frac {1}{N}}dN=\int {-\lambda }dt$
$ln(N)=-\lambda t+c$
$N=N_{0}e^{-\lambda t}$

## Deriving $t_{1/2}={\frac {ln2}{\lambda }}$

Half life is the time taken for half of the atoms that were originally present in the sample to have decayed.
$N_{(t)}=N_{0}e^{-\lambda t}$
If we replace $N_{0}$ with 1, $N_{t}$ with ${\frac {1}{2}}$, and t with $t_{\frac {1}{2}}$ we get:
${\frac {1}{2}}=e^{-\lambda t_{\frac {1}{-2}}}$
$-\lambda t_{\frac {1}{2}}=ln{\frac {1}{2}}$
$t_{\frac {1}{2}}={\frac {ln2}{\lambda }}$
If you wanted to know the ${\frac {1}{n}}$ of a substance, you can replace the two with a 'n'
$t_{\frac {1}{n}}={\frac {ln(n)}{\lambda }}$
# AQA A-Level Physics/Progressive waves

Progressive waves transfer energy from one point in space to another without the transfer of matter.