Jump to content

  • Log In with Google      Sign In   
  • Create Account


Like
15Likes
Dislike

Embedding Math Equations in Articles

By Michael Tanczos | Published Aug 02 2013 03:59 PM in Gamedev.net Help
Peer Reviewed by (Vilem Otte, Yrjö P., Josh Vega)

gdnethelp help math equations embed

Introduction


It's no secret that we at Gamedev.net have always been pretty heavy on the programming side of game development. The purpose of this article is to share some quick information on how to beef up your articles with all sorts of fancy pants math equations and formulas that will help others to understand your article topic better.

Background


First we want to give a special thanks to Tim Bright for pointing out MathJax to us. MathJax is a LaTeX and MathML javascript-based display engine that works in all browsers. We currently use the standard configuration of MathJax, so all examples will closely follow the documentation on their site.

Tutorial


Most of this article is based off of the tex samples located at http://www.mathjax.org/demos/tex-samples/ . The key to using formulas inside of your articles is to wrap any LaTeX or MathML formula in one of two special wrappers.

For multiline formulas use this:
\[ multiline formula goes here \]

For inline formulas and equations such as \(\sqrt{3x-1}+(1+x)^2\) you can use the following:
\( inline formula goes here \)


Quick Demo


The Lorenz Equations

\[\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned} \]

The Cauchy-Schwarz Inequality

\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]

A Cross Product Formula

\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix} \]

The probability of getting \(k\) heads when flipping \(n\) coins is

\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

An Identity of Ramanujan

\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

A Rogers-Ramanujan Identity

\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}. \]

Maxwell’s Equations

\[ \begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
\]

Demo Source


<b>The Lorenz Equations</b>

\[\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned} \]

<b>The Cauchy-Schwarz Inequality</b>

\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]

<b>A Cross Product Formula</b>

\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0
\end{vmatrix}  \]

<b>The probability of getting \(k\) heads when flipping \(n\) coins is</b>

\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]

<b>An Identity of Ramanujan</b>

\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

<b>A Rogers-Ramanujan Identity</b>

\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}. \]

<b>MaxwellÃÃÃÃâs Equations</b>

\[  \begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
\]


Conclusion


We hope this helps to build stronger, better, faster mathematics-based articles. Good luck and let us know if you come up with any issues.

Article Update Log


2 Aug 2013: Initial release



License


GDOL (Gamedev.net Open License)




Comments

Note: Please offer only positive, constructive comments - we are looking to promote a positive atmosphere where collaboration is valued above all else.




PARTNERS