Pizza theorem

Example of application of the theorem with eight sectors: by cutting the pizza along the blue lines and, alternately taking one slice each, proceeding clockwise or counterclockwise, two diners eat the same amount (measured in area) of pizza.
Proof without words for 8 sectors by Carter & Wagon (1994a).

In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way.

The theorem is so called because it mimics a traditional pizza slicing technique. It shows that if two people share a pizza sliced into 8 pieces (or any multiple of 4 greater than 8), and take alternating slices, then they will each get an equal amount of pizza, irrespective of the central cutting point.