Month: August 2012

I came accross this great tool for displaying mathematical equations the other day. MathJax not only supports \(\LaTeX\) syntax but also renders the equations as pure text, so no unsightly images and they scale beautifully. You can also right click on the equation and see it’s \(\LaTeX\) code.

The code for MathJax is open source, but if you don’t want to go to the bother of installing it yourself, you can use it on their CDN.

There are a couple of plugins to enable MathJax in WordPress. I’m using the Simple MathJax plugin. I’ve not tried the others.

To use MathJax simply mark up your equation with \[…\]. If you want to have an equation inline, use \(…\). You can also inline equations in the post title.

Here are a few examples taken from the MathJax site:

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}