It's pretty easy to divide a cake among two people so that each person thinks his piece is at least as good as the other: have one person divide the cake into two equal-looking pieces and have the other person pick one.

But how do you divide a cake among three people so that each person thinks his piece is at least as good as either of the other two? I'll describe an answer, due to Francis Su, which surprisingly is quite closely related to a basic fact from topology called the Brouwer fixed point theorem.