2004/03/02 by Louis H. Kauffman, Kauffman, Louis H. · 5 citations
Business, Management and Accounting · Engineering · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Law, logistics, and international trade #Mechanics and Biomechanics Studies #Robotic Mechanisms and Dynamics #math.GT
paper · pdf · doi:10.48550/arxiv.math/0403028
14 pages, 9 figures, LaTeX document
openalex publication_date 2004/03/02 · arxiv created 2004/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width) needed to tie the trefoil knot and the figure eight knot. The first conjecture states that (for width one) the least length of ribbon needed to tie an open-ended trefoil knot is L = 4(F + 1)/Sqrt[2 + F] where F = (1 + Sqrt[5])/2 is the golden ratio. The second conjecture states that the least length of the figure eight knot (in the same sense) is 32/Sqrt[15].