« Tau is Greater Than Pi
  
AsciiDoc Passthroughs, Hugo, LaTeX, and MathJax on Infinite Ink »

MathJax Kitchen Sink
Updated  2021-August-3

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News

2022-July-20  As of today, this evolving⁠[1] article has been on Infinite Ink for 1 year.🎂

About This Page

I’m using this page to test using MathJax in an article that’s written in AsciiDoc and generated by Hugo with help from the Asciidoctor Ruby gem. Most of this page was forked from parts of mathjax.github.io/MathJax-demos-web/ Thank you mathjax.org!

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To view the mathematical markup that produces any displayed formula on this page, right click the formula.
$$ \LaTeX $$

Quadratic Equation

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

Lorenz Equations

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

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

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

Probability of Getting \(k\) Heads When Flipping \(n\) Coins

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

An Identity of Ramanujan

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

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

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

Inline Mathematics

Finally, while display equations look good for a page of samples, the ability to mix mathematics and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.

 

See also

For more about mathematics, see Infinite Ink’s…

 

Endnote

1. Many Infinite Ink articles, including this one, are evergreen and regularly updated.

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