The Ham sandwich theorem, also known as the Stone-Tukey theorem in topology in mathematics, states that given n objects in n-dimensional space, it is possible to divide each one in half with a single (n − 1)-dimensional hyperplane.

It takes its name from the case when n=3 and the three objects of any shape are a chunk of ham and two chunks of bread — notionally a sandwich — which can then each be bisected with a single cut (i.e. a plane). In two dimensions, it is known as the pancake theorem of having to cut two infinitesimally thin pancakes on a plate each in half with a single cut (i.e. a straight line).

It has no relationship to the "squeeze theorem" (sometimes called the "sandwich theorem").