Comment by WCSTombs

To be fair, I'm constrained by plain text on Hacker News. The argument I wrote down requires a diagram to be fully understood, so I described it in words expecting the reader to draw it themselves, or at least mentally visualize it (for those used to doing it).

To be clear though, as far as I know every proof of the Pythagorean Theorem requires some sort of diagram, and the one I gave requires literally the least amount of drawing out of all the proofs (which is a bold claim, but call it a conjecture). That's why I felt comfortable writing out the proof just in words.