mermaid js

https://mermaid.js.org/
mermaid is a javascript based diagramming and charting tool.

Pie Chart

pie title Pets adopted by volunteers
    "Dogs" : 386
    "Cats" : 85
    "Rats" : 15

example: /md/mermaid/m.html

Math

graph LR
  A["$x^2 = 4$"]
  B["$x^2 = -4$"]
  C["$i = \sqrt{-1}$"]
  D["$x = \pm2i$"]
  E["$a + ib, \space where \space a, b \in {R}$"]

Complex Numbers

graph LR
  A["$2+3i$"]
  B["$-1-i$"]
  C["$\sqrt2+i\sqrt3$"]
  D["$(2+3i)+(4-8i)=$"]
  E["$(2+3i)+(4-8i)=6-5i$"]
  F["$-(2+3i)=-2-3i$"]
  G["$(2+3i)(4-8i)=8+12i-16i-24i^2=8+24-4i=32-4i$"]

Complex Conjugate

graph LR
  A["$a+ib=(a+ib)^* = a-ib$"]
  B["$(a+ib)(a-ib)=a^2+b^2$"]

Complex Numbers on the plane

graph LR
  A["$|a+ib| = \sqrt{a^2+b^2}=r$"]
  B["$a+ib = \frac{a+ib}{\sqrt{a^2+b^2}}$"]
  C["$a+ib = \frac{a}{\sqrt{a^2+b^2}} + i\frac{b}{\sqrt{a^2+b^2}}$"]

graph LR
  D["$a+ib = r(cos\theta+i sin\theta)$"]
  E["$tan \theta = \frac{b}{a}$"]
  F["$\theta = arctan (\frac{b}{a})$"]
  G["$a+ib=re^{i\theta}$"]

polar form

graph LR
  A["$a+ib = r(cos\theta+i sin\theta)$"]

exponential form

graph LR
  A["$a+ib=re^{i\theta}$"]

graph LR
  B["$1+i=\sqrt{2}(cos(\frac{\pi}{4})+i sin(\frac{\pi}{4}))=\sqrt{2}e^{i\frac{\pi}{4}}$"]

graph LR
  A["$2\sqrt{2}e^{i\frac{\pi}{4}}$"]
  A["$2\sqrt{2}e^{i\frac{-\pi}{2}}$"]
  A["$2\sqrt{2}e^{i\frac{3\pi}{4}}$"]

  A["$e^{i\frac{\pi}{5}}e^{i\frac{\pi}{3}} = e^{i\frac{8\pi}{15}}$"]

Matricies

graph LR
  A["$\begin{bmatrix}1\space -2\\0\space -10\end{bmatrix}$"]
  A["$\begin{bmatrix}1\\2\\-3\\8\end{bmatrix}$"]
  A["$\begin{bmatrix}5\space-2\space3\\7\space2\space1.5\end{bmatrix}$"]

m x n matrix

graph LR
  A["$\begin{bmatrix}1\space -2\space 3\\0\space -10\space 4\\1\space 2\space 3\end{bmatrix}$"]

  B["$\begin{pmatrix} 1 & 1 & 2 \\ -1 & 2 & 1 \ \end{pmatrix}$"]

  C["$\text{det} = 1(-1) - (-1)(2) = -1 + 2 = 1$"]