2022/08/05 by Elizabeth Denne, Denne, Elizabeth, Troy Larsen +1 · 3 citations
Mathematics · Engineering · #Geometric and Algebraic Topology #Advanced Materials and Mechanics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2208.03239
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 folded ribbon knot. The folded ribbon knot is also a framed knot, and the ribbon linking number is the linking number of the knot and one boundary component of the ribbon. We find the minimum folded ribbonlength for 3-stick unknots with ribbon linking numbers ±1 and ± 3, and we prove that the minimum folded ribbonlength for n-gons with obtuse interior angles is achieved when the n-gon is regular. Among other results, we prove that the minimum folded ribbonlength of any folded ribbon unknot which is a topological annulus with ribbon linking number ± n is bounded from above by 2n.