2004/05/04 by Louis H. Kauffman, Kauffman, Louis H.
Mathematics · Physics and Astronomy · #51F20 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #math.HO #msc:51F20
paper · pdf · doi:10.48550/arxiv.math/0405048
7 pages, 3 figures, LaTeX document
arxiv created 2004/05/04 · openalex publication_date 2004/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Is there any other proportion for a rectangle, other than the Golden Proportion, that will allow the process of cutting off successive squares to produce an infinite paving of the original rectangle by squares of different sizes? The answer is: No. The only proportion that allows this pattern is the Golden Ratio. Two proofs are given.