Comptes Rendus
Research article - Geometry and Topology
Constructing many-twist Möbius bands with small aspect ratios
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1837-1845.

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.

Cet article présente une construction d’un nœud de ruban de papier plié qui fournit une limite supérieure constante sur le rapport d’aspect infinitésimal pour les bandes de Möbius en papier et les anneaux avec un nombre arbitraire de demi-torsions. En particulier, la construction montre que les bandes de Möbius en papier et les anneaux avec un nombre arbitraire de demi-torsions peuvent être plongés avec un rapport d’aspect inférieur à 6.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.690
Classification: 49Q10, 51M16
Keywords: Möbius Band, Halpern–Weaver Conjecture, Folded Ribbon Knots Isometric Embedding, Optimization
Mots-clés : Bande de Möbius, conjecture de Halpern–Weaver, nœuds de rubans pliés Emboîtement isométrique, optimisation

Aidan Hennessey 1

1 69 Brown St., Mail# 3220, Providence, RI 02912, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRMATH_2024__362_G12_1837_0,
     author = {Aidan Hennessey},
     title = {Constructing many-twist {M\"obius} bands with small aspect ratios},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1837--1845},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.690},
     language = {en},
}
TY  - JOUR
AU  - Aidan Hennessey
TI  - Constructing many-twist Möbius bands with small aspect ratios
JO  - Comptes Rendus. Mathématique
PY  - 2024
SP  - 1837
EP  - 1845
VL  - 362
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.690
LA  - en
ID  - CRMATH_2024__362_G12_1837_0
ER  - 
%0 Journal Article
%A Aidan Hennessey
%T Constructing many-twist Möbius bands with small aspect ratios
%J Comptes Rendus. Mathématique
%D 2024
%P 1837-1845
%V 362
%I Académie des sciences, Paris
%R 10.5802/crmath.690
%G en
%F CRMATH_2024__362_G12_1837_0
Aidan Hennessey. Constructing many-twist Möbius bands with small aspect ratios. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1837-1845. doi : 10.5802/crmath.690. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.690/

[1] Brienne E. Brown; Richard E. Schwartz The Crisscross and the Cup: Two Short 3-Twist Paper Moebius Bands (2023) (https://arxiv.org/abs/2310.10000)

[2] Elizabeth Denne; Mary Kamp; Rebecca Terry; Xichen Zhu Ribbonlength of folded ribbon unknots in the plane, Knots, links, spatial graphs, and algebraic invariants (Contemporary Mathematics), Volume 689, American Mathematical Society, 2017, pp. 37-51 | DOI | MR | Zbl

[3] Elizabeth Denne; Troy Larsen Linking number and folded ribbon unknots, J. Knot Theory Ramifications, Volume 32 (2023) no. 1, 2350003, 42 pages | DOI | MR | Zbl

[4] B. Halpern; C. Weaver Inverting a cylinder through isometric immersions and isometric embeddings, Trans. Am. Math. Soc., Volume 230 (1977), pp. 41-70 | DOI | MR | Zbl

[5] Ana Jain; Mia Jain The Jain Conjecture for the Minimum Aspect Ratio of a Mobius Strip with Multiple Twists (2024) (https://drive.google.com/file/d/18N2fYFbTwWz0bStzACK7faz2b0BnYHc5/view)

[6] Richard E. Schwartz The Optimal Twisted Paper Cylinder (2023) (https://arxiv.org/abs/2309.14033)

[7] Richard E. Schwartz The Optimal Paper Moebius Band (2024) (to appear in Ann. Math.. https://arxiv.org/abs/2308.12641)

Cited by Sources:

Comments - Policy