Sometimes you discover a nice-looking path through the forest, and you follow it thinking it’ll lead you to some new, exciting place. But as you walk and walk amongst the trees, you come to realize it’s actually leading you somewhere you already knew. This article is a story about (re)discovery, and how new things can make us understand old things better.
Before we start, though, I want to make clear I’m in no way an “expert mathematician”. Every single piece of mathematical knowledge I’ve used in this article, I was taught in high school. And I have forgotten so much of it, in fact, that for the integrals in this article I had to resort to Wolfram Alpha every single time. ¯_(ツ)_/¯
This also means this article is likely to have innacuracies, and a fair share of things an actual mathematician would consider silly. For any such things (or anything else you want), you can reach me by email at jon at this domain, or on Twitter at jon_valdes.