Shading a Square (With Colors!) by Timmy Kelly ’24, Wednesday November 29, 1:00 – 1:50pm, North Science Building 113, Wachenheim
For which n can you cut a square into n triangles of equal area?
This question appears quite simple; it was even posed by the Ancient Greeks. But like many good puzzles, it is a remarkably stubborn one.
Despite the completely geometric nature of the question, Paul Monsky’s 1970 answer to it relies primarily on number theory and combinatorics! There is a small amount of algebraic machinery involved, but his proof is quite accessible, and we will work through it together (with an exploration of the P-adic number system along the way).