The ham sandwich theorem states that it is possible to divide a sandwich made up of three layers (ham, butter, bread) exactly in half with just one cut of the knife. Here's the mathematical formulation.

Theorem Given three bounded subsets of R3 there exists a plane in R3 dividing each of the subsets in half by volume.

The proof of the ham sandwich theorem is a corollary of the Borsuk-Ulam theorem.