[b][color=#000000]Napolean's Theorem![/color][/b][br]If [b][color=#ff7700]equilateral triangles[/color][/b] are built off the three sides off any original triangle, then the centroids of these [b][color=#ff7700]equilateral triangles[/color][/b] (or incenters or circumcenters or orthocenters[i]--aren't they all the same in an equilateral triangle?[/i]) will always form the vertices of yet [color=#38761d][b]another equilateral triangle![/b][/color]