Ribbonlength of folded ribbon unknots in the plane

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(π/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 √ 3, and such a minimizer is an equilateral triangle. We end the paper with a discussion of projection stick number and ribbonlength.