# Reforming Math

Here are my suggestions for making math notation better:

• Use $$\tau$$ instead of $$\pi$$ for the circle constant
• Instead of writing $$a_{12}$$ to mean the edge between points $$1$$ and $$2$$ in graph theory, write $$a_{1\leftrightarrow2}$$. Otherwise, it looks like indexing $$12$$ of $$a$$. When indexing a 2d-array, write $$a_{1,2}$$ instead of $$a_{12}$$. In a 100x100 array, $$a_{12}$$ should return a 1x100 vector (analogous to a[12]), not a number (analogous to a[1][2])
• A big source of confusion in math is not knowing what letter variables stand for. The problem with saying $$\text{charge}=\text{capacitance}\times \text{voltage}$$ is that it can be interpreted as $$c\times h\times a\times r\times g\times e=c\times a\times p\times a\times c\times i\times t\times a\times n\times c\times e\times v\times o\times l\times t\times a\times g\times e$$. The solution is to write a line over multiletter variables (inspired by the usage of the vinculum as a grouping operator).
Write $$\overline{\text{charge}}=\overline{\text{capacitance}}\ \overline{\text{voltage}}$$
If you want start the equation with a multiletter variable and use single-letter variables later, you can use $$\rm as$$, like so:
$\overline{\text{charge as Q}}=\overline{\text{capacitance as C}}\times\overline{\text{voltage as V}}$$V=\frac{Q}C$
• $$\sin^2(x)$$ should mean $$\sin(\sin(x))$$ and $$sin^{-1}(x)$$ should mean $$arcsin(x)$$ whereas
$$\sin(x)^2$$ should mean $$\sin(x)\cdot \sin(x)$$ and $$\sin(x)^{-1}$$ should mean $$\frac1{\sin(x)}$$
• Problem: $$(1, π)$$ can be a cartesian or polar coordinate.
Solution: make polar coordinates explicitly polar with a $$^p$$ superscript, such as $$(1, π)^p$$. You only have to do this if it is unclear.
• Use == when writing a proof, so that you remember that you cannot manipulate both sides like an equation. For example, prove $$\frac{\cos 2x-1}{\sin 2x}==-\tan x$$

### Reforming Physics

• Make an electron positive charge
• Use moles of e as a unit of charge instead of coulombs C because that way it is easier to visualize as opposed to being a completely arbitrary unit.
• Do not use \frac{1}{4\pi\epsilon_0}