Abstract
We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The folded ribbonlength is the length to width ratio of such a ribbon knot. We give upper bounds on the folded ribbonlength of 2-bridge, torus, twist, and pretzel knots, and these upper bounds turn out to be linear in the crossing number. We give a new way to fold torus knots and show that their folded ribbonlength is bounded above by . This means, for example, that the trefoil knot can be constructed with a folded ribbonlength of 6. We then show that any torus knot with has a constant , such that the folded ribbonlength is bounded above by . This provides an example of an upper bound on folded ribbonlength that is sublinear in crossing number.
Citation
Elizabeth Denne. John Carr Haden. Troy Larsen. Emily Meehan. "Ribbonlength of families of folded ribbon knots." Involve 15 (4) 591 - 628, 2022. https://doi.org/10.2140/involve.2022.15.591
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