On Nearly Optimal Paper Moebius Bands
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866910722559049728 |
|---|---|
| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | Let $ε<1/384$ and let
$Ω$ be a smooth embedded paper Moebius
band of aspect
ratio less than $\sqrt 3 + ε$. We prove that
$Ω$ is within Hausdorff distance
$18 \sqrt ε$ of an equilateral triangle of
perimeter $2 \sqrt 3$. This
is an effective and fairly sharp version of our recent theorems in [{\bf S0\/}] about
the optimal paper Moebius band. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Nearly Optimal Paper Moebius Bands Schwartz, Richard Evan Metric Geometry Let $ε<1/384$ and let $Ω$ be a smooth embedded paper Moebius band of aspect ratio less than $\sqrt 3 + ε$. We prove that $Ω$ is within Hausdorff distance $18 \sqrt ε$ of an equilateral triangle of perimeter $2 \sqrt 3$. This is an effective and fairly sharp version of our recent theorems in [{\bf S0\/}] about the optimal paper Moebius band. |
| title | On Nearly Optimal Paper Moebius Bands |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2412.00572 |