the pentagon, whirling triangles,
and the Archimedean spiral
This amazing number was known to Euclid and its properties have been studied through the ages, even to the present day. Now known as F (phi), it equals the sum of one plus its own reciprocal, or its own square minus one, but it approximates 1.61803... . At least one book has been written about it, and it has been said (probably wrongly) to have dictated the proportions of the Parthenon.
It can be shown to be the ratio of the side to the diagonal of a pentagon, so here we offer products showing "whirling triangles" in a pentagon, with an Archimedean spiral - the curve of every spiral shell - in gold, of course - touching their points.