The most beautiful formula not enough people understand

On the volumes of higher-dimensional spheres Explore the 3b1b virtual career fair: See https://3b1b.co/talent Become a supporter for early views of new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Thanks to UC Santa Cruz for letting me film there, and special thanks to Pedro Morales-Almazan for arranging everything. My video on Numberphile with a fun application of this problem: https://youtu.be/6_yU9eJ0NxA Timestamps: 0:00 - Introduction 1:01 - Random puzzle 6:16 - Outside the box 14:35 - Setting up t