On The Optimal Paper Moebius Band
Metric Geometry
2023-09-12 v3
Abstract
Let . There are two main conjectures about paper Moebius bands. First, a smooth embedded paper Moebius band must have aspect ratio at least A. Second, any sequence of smooth embedded paper Moebius bands having aspect ratio converging to A converges, in the Hausdorff topology and up to isometries, to an equilateral triangle of semiperimeter A. We will reduce these conjectures to 10 statements about the positivity of certain explicit piecewise algebraic expressions.
Keywords
Cite
@article{arxiv.2012.07783,
title = {On The Optimal Paper Moebius Band},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2012.07783},
year = {2023}
}
Comments
This paper is completely superseded by my new paper, "The Optimal Paper Moebius Band" (arXiv:2308.12641) The new paper solves the conjecture that the now withdrawn paper made partial progress towards and thereby renders the withdrawn paper irrelevant