Alice, Bob, and the Average Shadow of a Cube

Embark on a 40-minute mathematical journey exploring the average shadow of a cube through the problem-solving approaches of two characters, Alice and Bob. Delve into complex geometric concepts, including Bertrand's paradox and Cauchy's theorem on convex solids. Follow along as the video breaks down the problem-solving process, from initial thoughts to piecing together the cube, and compare the different conclusions reached by Alice and Bob. Gain insights into effective problem-solving strategies and challenge yourself with the provided homework. Enhance your understanding of 3D geometry, shadows, and mathematical reasoning in this engaging and informative presentation.

, I say "divide the total by 1/2", but of course meant to say "multiply...".
- The players.
- How to start.
- Alice's initial thoughts.
- Piecing together the cube.
- Bob's conclusion.
- Alice's conclusion.
- Which is better?.
- Homework.