Check out the attachment
The triangle makes use of the properties of the Fibonacci numbers. Notice that the triangle is of has sides 13 and 5 (Fibonacci). In particular it is possible to show that (Fn)^2 (the nth Fibonacci number squared) differs from F(n-1) x F(n+1) by 1 always. Sometimes + 1 sometimes - 1. The triangle you show just plays on this. Have a look at a 21 x 21 square and a 34 x 13 rectangle.