26 Nov '12 00:17>3 edits
Prove that if a hexagon is dissected into identical equilateral triangles, and these triangles are rearranged into smallr hexagons (6 triangles to a small hexagon) then you always get a square number of small hexagons.
Originally posted by forkedknightAn equilateral triangle also divides into 9 smaller ones, ... or 16, ... or 25.
As far as I know, the only way to disect an equilateral triangle into smaller equilateral triangles is to cut it into a triforce, resulting in 4 smaller triangles.
4 is a square number.
The simplest way to dissect a hexagon into equilateral triangles results in 6 triangles.