A Unified Theory of Proportion

Jay Kappraff and Gary W. Adamson
Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings (2003)
Pages 161–172


Key elements of the systems of proportions used in ancient sacred geometry will be shown to be the ratio of diagonal to edge of various of regular n-gon. The diagonals are shown to be edges of various species of star polygons related to the n-gon. These diagonals or edges are shown to be the roots of two species of polynomials derived from Pascal's triangle and related to the Fibonacci and Lucas sequences when the n-gon has unit radius. All diagonals of regular n-gons are shown to have additive properties. Special attention is given to the heptagon.