Constructing many-twist Möbius bands with small aspect ratios

Constructing many-twist Möbius bands with small aspect ratios

This paper presents a construction of a folded paper ribbon knot that provides a constant upper bound on the infimal aspect ratio for paper Möbius bands and annuli with arbitrarily many half-twists. In particular, the construction shows that paper Möbius bands and annuli with any number of half-twis...

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Bibliographic Details
Main Author: Hennessey, Aidan
Format: Article
Language:English
Published: Académie des sciences 2024-11-01
Series:Comptes Rendus. Mathématique
Subjects:
Möbius Band
Halpern–Weaver Conjecture
Folded Ribbon Knots Isometric Embedding
Optimization
Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.690/
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Summary:This paper presents a construction of a folded paper ribbon knot that provides a constant upper bound on the infimal aspect ratio for paper Möbius bands and annuli with arbitrarily many half-twists. In particular, the construction shows that paper Möbius bands and annuli with any number of half-twists can be embedded with aspect ratio less than 6.
ISSN:1778-3569

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