Description:

A proof that all composite integers are equal to a (nontrivial) sum of integer squares. This uses a the standard proof of phi's irrationality as a justification for representing a composite number as a rectangle with side lengths > 1 that can be decomposed into a set of squares. The area of the original rectangle is equal to the sum of all of the areas of the squares, so every composite number is equal to a sum of squares that are not all 1. Written in Latex using tikz by Garrett Credi.