Monday, July 20, 2009

geometry - pizza theorem

The Pizza Theorem: If a circular pizza is cut by four straight cuts into eight slices whose tips have the same angle and come to the same point somewhere on the surface of the pizza, then the sum of the areas of alternating slices is equal to half the area of the pizza. This sketch gives a 'visual proof' of this neat idea. I have used it as part of a discussion of mathematical proof. While this is not a proof, it is a very convincing display and it can certainly offer some amount of insight into the problem. The evidence put forth by this sketch is more accessible and interesting to most people than any analytical approach. The sketch is dynamic in that the 'center' can be moved and the rays can be rotated to allow the exploration of different scenarios. The proof relies on the tilting or shearing of triangles, which is briefly explained on an additional page of the sketch.
Keywords: gsp presentation, animation, pizza theorem, visual proof, shearing


  1. What an awesome sketch. I am fascinated that someone could visualize this WITHOUT the sketch.