An improved bound for the optimal paper Moebius band

TL;DR

This paper establishes a new lower bound for the aspect ratio of smoothly embedded Moebius bands, improving upon the previous bound and involving an optimization-derived algebraic number.

Contribution

It provides a tighter lower bound on the aspect ratio of smoothly embedded Moebius bands, advancing geometric understanding.

Findings

New lower bound: at least rac{rac{3}{2}}

Improves previous bound of rac{rac{pi}{2}

Bound involves an algebraic number from optimization

Abstract

In this paper we show that a smoothly and locally isometrically embedded Moebius band has aspect ratio at least $\sqrt 3-(1/26)$. (The actual bound, an algebraic number that arises in an optimization problem, is a tiny bit better.) Our bound improves significantly on the previous known lower bound of $\pi/2$.