On a Better Golden Rectangle (That is Not 61.8033…% Useless!)
Douglas McKenna

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
Pages 187–194
Regular Papers

Abstract

In which (A) it is alliteratively alleged that the φ×1 Golden RectangleTM is a φction of self-referential spatial elegance, unworthy of the reverent φxation with which φlosophers of beauty have for too long worshipped it; and (B) it is deφnitively demonstrated that the √ φ×1 rectangle is a far more satisφing, lean, golden mean, æsthetic φst-φghting machine. We explore its recursive subdivision into self-tilings exhibiting emergent global structure and patterns, and show its relationship both to golden ratio-based identities and to Ammann’s bee tile, with a little art phistory added.

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Updates

10 December 2018

This version corrects a minor mathematical typo, provides colour versions of all the illustrations, and updates a stale URL reference to a current one.