# The Theorem of Napoleon

Submitted by Structure on Sun, 12/16/2007 - 19:42.

Let ABC be a triangle. Let us construct three equilateral triangles on the sides of the ABC triangle in the exterior of the triangle (A_{1}BC, AB_{1}C and ABC_{1}). Let A_{2}, B_{2} and C_{2} be the centroids of these three triangles. Then A_{2}B_{2}C_{2} is an equilateral triangle.