Mathematical Typesetting Test

This page tests the mathematical typesetting capabilities of the site, which are powered by KaTeX.

Note: For this to render correctly, KaTeX support must be enabled in your site’s configuration. See the Hugo documentation for details.

Inline Formulas

Mathematical formulas can be included directly in a sentence. For example, the famous Pythagorean theorem is written as \( a^2 + b^2 = c^2 \). Another common inline formula is Euler’s identity, \( e^{i\pi} + 1 = 0 \), which beautifully connects five fundamental mathematical constants.

Block-Level Formulas

For more complex or important formulas, it’s better to display them on their own line.

The quadratic formula is a staple of algebra: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

The definition of the Fourier Transform shows an integral: \[ \hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-2\pi i \xi x}\ dx \]

A summation can be written as: \[ \sum_{i=1}^{n} i = \frac{n(n+1)}{2} \]

We can also render a matrix: \[ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} \]

And finally, a full representation of Maxwell’s Equations in a vacuum: \[ \begin{align*} \nabla \cdot \vec{E} &= 0 \ \nabla \cdot \vec{B} &= 0 \ \nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \ \nabla \times \vec{B} &= \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t} \end{align*} \]

If all the formulas above are rendered correctly, the KaTeX integration is working perfectly.