A Better Nature

http://commons.wikimedia.org/wiki/File:Morley_Proof.svg

Trisect the angles of any triangle and you’ll find an equilateral triangle at its heart.

This theorem has a curious cousin: If you trisect the sides of any triangle and erect an equilateral triangle outwardly on the middle third of each leg, then the outermost vertices of these equilateral triangles will themselves form an equilateral triangle.