2000 character limit reached
Constructing many-twist Möbius bands with small aspect ratios
Published 26 Jan 2024 in math.GT and math.DG | (2401.14639v2)
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.
- Ribbonlength of folded ribbon unknots in the plane. Knots, links, spatial graphs, and algebraic invariants, 2017.
- Linking number and folded ribbon unknots. The Journal of Knot Theory and its Ramifications, 2023.
- Halpern and Weaver. Inverting a cylinder through isometric immersions and embeddings. Transactions of the American Mathematical Society, 1977.
- Richard E. Schwartz. The optimal paper moebius band. 2023.
- Richard E. Schwartz. The optimal twisted paper cylinder. 2023.
- The crisscross and the cup: Two short 3-twist paper moebius bands. 2023.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.