Mathematics in Web Publishing

One of the challenges of technical writing on the web is properly rendering mathematical notation. With KaTeX, we can render both inline and display math beautifully.

Inline Math

The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ is one of the most well-known formulas in mathematics. We can also write Euler’s number $e \approx 2.71828$ inline.

Display Math

Euler’s identity is often cited as the most beautiful equation:

$$e^{i\pi} + 1 = 0$$

The Gaussian integral:

$$\int_{-\infty}^{\infty} e^{-x^2}, dx = \sqrt{\pi}$$

A matrix equation:

$$\begin{pmatrix} a & b \ c & d \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} ax + by \ cx + dy \end{pmatrix}$$

Code and Math Together

Here’s a Python function that computes the Gaussian function:

import math

def gaussian(x, mu=0, sigma=1):
    """Compute the Gaussian function."""
    coefficient = 1 / (sigma * math.sqrt(2 * math.pi))
    exponent = -0.5 * ((x - mu) / sigma) ** 2
    return coefficient * math.exp(exponent)

# The integral of this function over all reals equals 1
print(gaussian(0))  # Peak value at mean

The function above computes $f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$ which is the probability density function of the normal distribution.