Math Typesetting with KaTeX

as-folio uses KaTeX to render LaTeX mathematics. Enable it per-post with math: true in the frontmatter.

Inline math

Write inline math between single dollar signs: $...$. For example, the energy-mass equivalence $E = mc^2$ is one of the most famous equations in physics.

The Euler identity $e^{i\pi} + 1 = 0$ is often cited as the most beautiful equation in mathematics.

Display equations

Use double dollar signs for display (block) equations:

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$$ $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

These are two of Maxwell’s equations for electromagnetism.

Fractions and integrals

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

The Lorentz factor from special relativity:

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

Matrices

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

Aligned equations

The derivation of general relativity’s field equations:

$$\begin{aligned} G_{\mu\nu} + \Lambda g_{\mu\nu} &= \kappa T_{\mu\nu} \\ \kappa &= \frac{8\pi G}{c^4} \end{aligned}$$

where $G_{\mu\nu}$ is the Einstein tensor, $\Lambda$ is the cosmological constant, $g_{\mu\nu}$ is the metric tensor, and $T_{\mu\nu}$ is the stress-energy tensor.