Highlight this Highlight this Highlight this 
Move the slider to rotate the square.

Highlight this Highlight this Highlight this 
(This paragraph will be easier to follow if the slider is pulled to the right.) The inner square has side a and the outer square has side a√5, so b  a, the short side of the colored rectangles, is a(√5  1)/2. The long side, b, is a(√5 + 1)/2. Therefore
τ = b/a = (√5 + 1)/2, and
ρ = a/b = (ba)/a = (√5  1)/2.