Pythagorean
Mysteries....

Penrose Tilings, the
Golden Rectangle, and the Pentagram share geometric properties having to do
with the ratio "phi":

j = (1+ 5^{1/2})/2 = 1.618....

Examples of Penrose
tilings are shown in the background images. While the golden rectangle has the
following shape (which is inscribed internally to indicate
its iterative geometric properties):

Golden
Rectangle

A pentagram you've
seen (the red star between white and yellow pentagons):

Pentagram