Math Rendering Test Fixture
Inline Math
Einstein's famous equation $E = mc^2$ relates energy and mass.
The quadratic formula gives $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for any quadratic.
Euler's identity: $e^{i\pi} + 1 = 0$ is often called the most beautiful equation.
For a circle of radius $r$, the area is $A = \pi r^2$ and circumference is $C = 2\pi r$.
Display Math: Fractions
$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$
$$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$$
Display Math: Integrals
$$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$
$$\oint_C \mathbf{F} \cdot d\mathbf{r} = \iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}$$
Display Math: Sums & Products
$$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$$
$$\prod_{i=1}^{n} x_i = x_1 \cdot x_2 \cdots x_n$$
Display Math: Matrices
$$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax + by \\ cx + dy \end{pmatrix}$$
$$\det\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix}$$
Greek Letters
Lowercase: $\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu$
More: $\nu, \xi, \pi, \rho, \sigma, \tau, \upsilon, \phi, \chi, \psi, \omega$
Uppercase: $\Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Phi, \Psi, \Omega$
Subscripts & Superscripts
$x_1, x_2, \ldots, x_n$ and $a^{n+1}$
Nested: $e^{x^2}$ and $a_{i_j}$
Display Math: Limits
$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$