Joint C&O/PureMath Colloquium - Hayley Reid

Title: Cutting a square into triangles of equal area

Abstract:

Suppose you are given a square and asked to cut it into n triangles of equal area. If n is even the problem is almost trivial, but when n is odd the problem becomes much harder. It turns out that it is impossible to cut a square into an odd number of triangles of equal area, and the proof of this is what makes this topic so interesting. It is the only known proof, and it involves valuations, a colouring of the plane, and some combinatorial reasoning. In this talk, we will cover the basics of valuations, and see an overview of the proof.