The Optimal Paper Moebius Band
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917801497722880 |
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| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than $\sqrt 3$. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to $\sqrt 3$ must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12641 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Optimal Paper Moebius Band Schwartz, Richard Evan Metric Geometry In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than $\sqrt 3$. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to $\sqrt 3$ must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977. |
| title | The Optimal Paper Moebius Band |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2308.12641 |