Affiliation:
1. Department of Mathematics, Washington & Lee University, Lexington, VA 24450, USA
Abstract
We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot. We show for any knot or link type that there exist constants [Formula: see text] such that the ribbonlength is bounded above by [Formula: see text], and also by [Formula: see text]. We use a different method for each bound. The constant [Formula: see text] is quite small in comparison to [Formula: see text], and the first bound is lower than the second for knots and links with [Formula: see text] 12,748.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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1. Folded ribbonlength of 2-bridge knots;Journal of Knot Theory and Its Ramifications;2023-04
2. Linking number and folded ribbon unknots;Journal of Knot Theory and Its Ramifications;2023-01
3. Ribbonlength of families of folded ribbon knots;Involve, a Journal of Mathematics;2022-12-31