Ribbonlength of folded ribbon unknots in the plane

Elizabeth Denne; Mary Kamp; Rebecca Terry; Xichen; Zhu

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arXiv · 1602.08084

Ribbonlength of folded ribbon unknots in the plane

Elizabeth Denne·Mary Kamp·Rebecca Terry·Xichen·Zhu

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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 ribbon, and it turns out that the way the ribbon is folded influences the ribbonlength. We give an upper bound of $n\cot(\pi/n)$ for the ribbonlength of $n$-stick unknots. We prove that the minimum ribbonlength for a 3-stick unknot with the same type of fold at each vertex is $3\sqrt{3}$, and such a minimizer is an equilateral triangle. We end the paper with a discussion of projection stick number and ribbonlength.

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BibTeX RIS

Elizabeth Denne, Mary Kamp, Rebecca Terry, Xichen, Zhu. 2016-02-25. Ribbonlength of folded ribbon unknots in the plane. https://arxiv.org/abs/1602.08084

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