Mathematics – Geometric Topology
Scientific paper
2004-03-02
Mathematics
Geometric Topology
14 pages, 9 figures, LaTeX document
Scientific paper
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].
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