One of the things I’ve always enjoyed about moving farther in mathematics is being able to understand/process old information from a variety of different contexts. Of course, I’m still no Benson Farb (if you’ve never heard Benson talk about the insolvability of the quintic using algebro-geometric machinery, you’re really missing out), but I really do enjoy learning new ways to visualize things I’ve known for a while.
For example, there’s a novel trapezoidal proof of the Pythagorean Theorem that makes sense if you know simple things like the area of a right trapezoid:
. Seeing stuff like that makes me happy, and it makes me realize:
It could be fun/worthwhile to begin a blog post series of Interesting Proofs which outlines various “interesting” proofs of fundamental(-ish) mathematical facts. I’m imagining a recurring series of blog posts connected only by the fact that they’re novel proofs of things that most people have known since adolescence.
You guys should chime in to tell me whether you’d be interested in anything like that. Pretends people actually read this nonsense