Consider a ham sandwich, consisting of two pieces of bread and one of ham.

geometry/ham.sandwich

Problem

Consider a ham sandwich, consisting of two pieces of bread and one of
ham.  Suppose the sandwich was dropped into a machine and spindled,
torn and mutilated.  Is it still possible to divide the ham sandwich
with a straight knife cut such that both the ham and each slice of
bread are divided in two parts of equal volume?

Show solution

Yes.  There is a theorem in topology called the Ham Sandwich Theorem,
which says: Given 3 (finite) volumes (each may be of any shape, and in
several pieces), there is a plane that cuts each volume in half.  You
would learn about it typically in a first course in algebraic topology,
or maybe in a course on introductory topology (if you studied the
fundamental group).