I went to an entertaining talk by UCI theorist and computational geometer David Eppstein yesterday. He showed some proofs (the subject was far afield for me, but engaging), some of which employed the Happy Ending Theorem. (Dr. Eppstein also seems to have written much of that Wikipedia entry.) The statement of the theorem goes like this:

Theorem. Any set of five distinct points in the plane such that no three are in a line has a subset of four points that form the vertices of a convex quadrilateral.

The proof is due to Esther Klein, and shortly after she showed the proof to them, Paul Erdős and George Szekeres produced a generalization.

The obvious question is, “So what’s this got to do with happy endings?” It turns out that it was named the Happy Ending Theorem by Erdős, because it resulted in the marriage of his friends Klein and Szekeres.

How adorable is that? One-hundred percent adorable.

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