Ham sandwich theorem
Theorem that any three objects in space can be simultaneously bisected by a plane / From Wikipedia, the free encyclopedia
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Not to be confused with the squeeze theorem (sometimes called the "sandwich theorem").
In mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide each one of them in half (with respect to their measure, e.g. volume) with a single (n − 1)-dimensional hyperplane. This is even possible if the objects overlap.
It was proposed by Hugo Steinhaus and proved by Stefan Banach (explicitly in dimension 3, without taking the trouble to state the theorem in the n-dimensional case), and also years later called the Stone–Tukey theorem after Arthur H. Stone and John Tukey.