Mathematics of slicing pizza


(photo by Randy Son Of Robert)

For almost twenty years, mathematicians Rick Mabry and Paul Deiermann have attempted to figure out the perfect way to slice a pizza for sharing. Turns out, mathematicians have been pondering pizza slicing problems since at least the 1960s. Mabry and Diermann have recently proved their pizza theorem and are now considering other related problems, like what happens if the pizza is square or, say, a 3D pizza, aka a calzone? From New Scientist:

Suppose the harried waiter cuts the pizza off-centre, but with all the edge-to-edge cuts crossing at a single point, and with the same angle between adjacent cuts. The off-centre cuts mean the slices will not all be the same size, so if two people take turns to take neighbouring slices, will they get equal shares by the time they have gone right round the pizza – and if not, who will get more?

Of course you could estimate the area of each slice, tot them all up and work out each person's total from that. But these guys are mathematicians, and so that wouldn't quite do. They wanted to be able to distil the problem down to a few general, provable rules that avoid exact calculations, and that work every time for any circular pizza.

"The perfect way to slice a pizza"