Alice, Bob, and the average shadow of a cube

A tale of two problem solvers. Numberphile video on Bertrand’s paradox: Help fund future projects: ​ Special thanks to these supporters: #thanks An equally valuable form of support is to simply share the videos. Curious why a sphere’s surface area is exactly four times its shadow? If you liked this topic you’ll also enjoy Mathologer’s videos on very interesting cube shadow facts: Part 1: Part 2: