A Biological Basis for the Golden Section in Art and Design

Abstract

artists have produced intuitively many of these complex rhythms. Architecture in particular gives great opportunities for symmetrical rhythms [15]. Egyptian artists had intuitively discovered all 17 symmetry groups. Hermann Weyl, the mathematician, says of the Egyptians: One can hardly overestimate the depth of geometric imagination and inventiveness reflected in these patterns. Their construction is far from being mathematically trivial. The art of ornament contains in implicit form the oldest piece of higher mathematics known to us. To be sure the 62 McWhinnie, Biological Basis for the Golden Section in Art and Design This content downloaded from 207.46.13.120 on Wed, 14 Sep 2016 05:48:02 UTC All use subject to http://about.jstor.org/terms conceptual means for a complete abstract formulation of the underlying problem, namely the mathematical notion of a group of transformations, was not provided before the nineteenth century; and only on this basis is one able to prove that the 17 symmetries already implicitly known to the Egyptian craftsman exhaust all possibilities [16]. THE GOLDEN SECTION AND