A tale of two problem solvers (Average cube shadows)

What's the average area of a cube's shadow? Numberphile video on Bertrand's paradox:    • Bertrand's Paradox (with 3blue1brown)...   Help fund future projects:   / 3blue1brown   An equally valuable form of support is to simply share the videos. There's a small error at 19:30, I say "Divide the total by 1/2", but of course meant to say "Multiply..." Curious why a sphere's surface area is exactly four times its shadow?    • But why is a sphere's surface area fo...   If you liked this topic you'll also enjoy Mathologer's videos on very interesting cube shadow facts: Part 1:    • The cube shadow theorem (pt.1): Princ...   Part 2:    • The cube shadow theorem (pt.2): The b...   I first heard this puzzle in a problem-solving seminar at Stanford, but the general result about all convex solids was originally proved by Cauchy. Mémoire sur la rectification des courbes et la quadrature des surfaces courbes par M. Augustin Cauchy
The artwork in this video was done by Kurt Bruns Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Hindi: rajeshwar-pandey ------------------- Timestamps 0:00 - The players 5:22 - How to start 9:12 - Alice's initial thoughts 13:37 - Piecing together the cube 22:11 - Bob's conclusion 29:58 - Alice's conclusion 34:09 - Which is better? 38:59 - Homework ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here:


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Music by Vincent Rubinetti.
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