Folded ribbon knots in the plane
Elizabeth Denne

TL;DR
This survey explores folded ribbon knots in the plane, focusing on ribbonlength minimization, known bounds, and how folding choices influence the minimal length for various knot types.
Contribution
It summarizes existing results on ribbonlength bounds, discusses the impact of folding choices, and compares different folded ribbon equivalence types.
Findings
Upper bounds for twist and torus knots' ribbonlength
Ribbonlength bounds relate to crossing number
Fold choice affects ribbonlength
Abstract
This survey reviews 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 ribbon, and the ribbonlength problem asks to minimize the ribbonlength for a given knot type. We give a summary of known results. For the most part, these are upper bounds of ribbonlength of twist knots and certain families of torus knots. We discuss result of G. Tian, which give upper bounds of ribbonlength in terms of crossing number. In addition, it turns out the choice of fold affects the ribbonlength. We end with a discussion of three different types of folded ribbon equivalence and give examples illustrating their relationship to ribbonlength.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Materials and Mechanics
