Hmmm. While contemplating my previous entry about little things not typically making me either any happier or any less happy, I seem to have accidentally proved a theorem in geometry. Oddly this has made me happier, because geometric theorems are shiny :-)

(Consider a polygon, and a point moving around inside it. Consider the sum of the shortest distances from the point to each side of the polygon. Theorem: if the polygon is regular, then this sum remains completely constant no matter where the point moves inside it. Proof, and relevance to my emotional life, left as exercises for the reader…)