Constructing many-twist M\"obius bands with small aspect ratios

Abstract

This paper presents a construction of a folded paper ribbon knot that provides a constant upper bound on the infimal aspect ratio for paper M\"obius bands and annuli with arbitrarily many half-twists. In particular, the construction shows that paper M\"obius bands and annuli with any number of half-twists can be embedded with aspect ratio less than 8.