Cracking the Pythagorean Code: The Quest for a Trigonometry Proof

In December 2022, seniors Micaiah Jackson and Kelsey Johnson were working on a school wide math contest that came with a cash prize. I was motivated because there was a monetary incentive, cause I was like, $500 is a lot of money, so I would like to at least try. Both were staring down the thorny bonus question. So tell me, what was this bonus question? It was to create a new proof of the Pythagorean theorem, and it kind of gave you a few guidelines on how would you start a proof. The seniors were familiar with the Pythagorean theorem, a fundamental principle of geometry. You may remember it from high school. A squared plus B squared equals C squared. In plain English, when you know the lengths of two sides of a right triangle, you can figure out the length of the third. Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told them was there’d been more than 300 documented proofs of the Pythagorean theorem using algebra and geometry. But for 2,000 years, a proof using trigonometry was thought to be impossible. And that was the bonus question facing them. When you looked at the question, did you think, boy, this is hard? Yeah. Yeah. What motivated you to say, well, I’m gonna try this? I think I was like, I started something, I need to finish it. So you just kept on going? Yeah. For two months. That Winter they spent almost all their free time working on the proof.