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.
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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
@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}, }
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/
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