Mathologer

Pi is IRRATIONAL: simplest proof on toughest test (2018x2)

Air date: Feb 03, 2018

In the last video of 2017 I showed you Lambert’s long but easy-to-motivate 1761 proof that pi is irrational. For today’s video Marty and I have tried to streamline an ingenious proof due to the famous French mathematician Charles Hermite into the hopefully simplest and shortest completely self-contained proof of the irrationality of pi. There are a few other versions of this proof floating around and we’ve incorporated the best ideas from these versions into what I’ll show you today; I’ll list some of these other versions below. I also talk about the problem of pi + e and pi x e being irrational at the end of the video, really nice stuff.