Lessons from my #proofinatoot writing:

1. The mastodon interface has no markdown preview; can admins add one? For example, here's one: https://kerzol.github.io/markdown-mathjax/editor.html

2. Greek letters are *expensive*; latex \(\alpha\) is 6 characters, plus 4 for math mode. Unicode α is only 1.

3. All those extra spaces in my easy-to-read latex source add up!

Pythagorean Theorem #proofinatoot

0. Subdivide a right triangle into two smaller right triangles.

1. \(\alpha+\tau = 90 = \sigma+\tau\) so \(\alpha = \sigma\). Likewise \(\beta = \tau\).

Hence the three triangles are similar.

2. By similarity,

\[\frac{s}{a}=\frac{a}{c}, \quad \frac{t}{b} = \frac{b}{c}.\]

3. By construction \(c = s + t\).

4. Combining these, we have

\[c = \frac{a^2}{c} + \frac{b^2}{c},\]

therefore

\[

c^2 = a^2 + b^2.

\]

Joined May 2017