The Optimal Paper Moebius Band
Metric Geometry
2024-10-15 v9
Abstract
In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than . We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977.
Cite
@article{arxiv.2308.12641,
title = {The Optimal Paper Moebius Band},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2308.12641},
year = {2024}
}
Comments
This paper has been accepted for publication by the Annals of Mathematics. This is the final version, the one I am publishing. This differs from the previous version in two ways: I removed an appendix and I changed the typesetting to the journal's specs