Visualizing Affine Regular, Area-Preserving Decompositions of Irregular 3D Pentagons and Heptagons
Douglas G. Burkholder

Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture
Pages 333–336
Short Papers

Abstract

We demonstrate a simple, elegant, and visual method for decomposing irregular pentagons into a pair of affine images of the two distinct types of regular pentagons. Moreover, the sum of the area of the two affine images equals the area of the original irregular pentagon. Similarly, we decompose irregular heptagons into a triple of affine images of the three distinct types of regular heptagons. One can use these decompositions to design visually interesting sculptures reflecting these geometric relationships.

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