The optimal paper Moebius band

• 成果类型: Article
• 署名作者: Schwartz, R. I. C. H. A. R. D. EvAN
• 署名单位: Brown University
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2025.201.1.5
• 发表日期: 2025-01
• 页码: 291-305
• 关键词: optimal Moebius band; Halpern-Weaver conjecture; developable surfaces; Tpatterns; MOBIUS; ROPELENGTH; shape

摘要

We prove that a smooth embedded paper Moebius band must have aspect ratio greater than \/3. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to \/3 must converge, up to isometry, to the triangular Moebius band. These results answer the mimimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B. Halpern and C. Weaver from 1977.