Ribbonlength and crossing number for folded ribbon knots

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.