Monsky's theorem

In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection.

The problem was posed by Fred Richman in the American Mathematical Monthly in 1965, and was proved by Paul Monsky in 1970.

Monsky's proof combines combinatorial and algebraic techniques, and in outline is as follows:

The theorem can be generalized to higher dimensions: an n-dimensional hypercube can only be divided into simplices of equal volume, if the number of simplices is a multiple of n!.

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