Pentagon Inside the Circle of Willis and the Golden Ratio

Abstract

The Golden ratio ("phi" or "Ф") has been known to us for ages and its use in art and architectural designs has enhanced its exquisiteness. Even some of the astounding creations of nature do follow this principle of Golden or divine proportions. Three centuries ago the circle of Willis at the base of the brain was first described and illustrated by Thomas Willis. Classically it was described as being circular in shape, however, the gross anatomy reveals a slightly different picture. The components of this complex neurovascular structure are so arranged that it appears more like a pentagon than a circle. A regular pentagon, unlike a circle, is a Golden shape that mathematically obeys the laws of Golden proportions. Like most other marvelous structures in nature, the close resemblance of the circle of Willis to a pentagon is more of a conscious effort of nature to establish consonance with aesthetic perception, rather than just a mere coincidence.

Keywords: Circle of Willis; Divine proportion; Golden proportions; Golden ratio; Golden shapes; Pentagon; Phi.