Derived from easyasme.com/Joe

Axiom of power set

De Morgan's law

Quadratic Formula

Binomial Coefficient

Sophomore's dream

Divergence

Complex number

Moore determinant

Sphere volume

Spherical coordinates derivation of the volume of a sphere $\left(\frac{4}{3}\pi R^3\right)$ .
The formula $S$ for a sphere of radius $R$ in spherical coordinates is:
$S=\left\{0\le \varphi \le 2\pi ,0\le \theta \le \pi ,0\le \rho \le R\right\}$ $$\begin{array}{rl}\text{Volume}& =\underset{S}{\iiint }{\rho }^{2}sin\theta d\rho d\theta d\varphi \\ & ={\int }_0^{2\pi }d\varphi {\int }_0^{\pi }sin\theta d\theta {\int }_0^R{\rho }^{2}d\rho \\ & =\varphi {|}_0^{2\pi }\left(-\cos \theta \right){|}_0^{\pi }\frac{1}{3}{\rho }^3{|}_0^R\\ & =2\pi \times 2\times \frac{1}{3}{R}^3\\ & =\frac{4}{3}\pi R^3\end{array}$$

Schwinger-Dyson equation

Differentiable Manifold (tangent vector)

Cichoń's Diagram

Multiscripts & greek alphabet

nested roots

nested matrices

font sizes