Math & KaTeX

Inline Math

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, used to solve any quadratic equation.

Euler’s identity, $e^{i\pi} + 1 = 0$, is considered one of the most beautiful equations in mathematics.

The Pythagorean theorem states that $a^2 + b^2 = c^2$ for any right triangle.

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Block Math

The Gaussian integral:

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

Maxwell’s equations in differential form:

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

A matrix expression:

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

The definition of a limit:

$$ \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e $$