Question

If you cut a pizza into 45 degree wedges meeting at a point other than the center and two people eat alternative slices, do they each get the same amount?

Answer 1

Surprisingly, if you make 4 slices, the answer is no. But if you make 8 slices as wanted, the answer is yes. A google search on "pizza 45 degree slices" turns up a book on google books named "Which way did the bicycle go?"

It contains a nice article which shows that you can use calculus and polar coordinates to prove it.