The Optimal Twisted Paper Cylinder
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866912599756505088 |
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| author | Montgomery, Noah Schwartz, Richard Evan |
| author_facet | Montgomery, Noah Schwartz, Richard Evan |
| contents | An embedded twisted paper cylinder of
aspect ratio $λ$ is a smooth isometric
embedding of a flat $λ\times 1$
cylinder into $\R^3$ such that the
images of the boundary components
are linked. We prove that for such
an object to exist we must have
$λ>2$ and that this bound is sharp.
We also show that any sequence of examples
having aspect ratio converging to $2$
must converge to a (non-smooth)
$4$-fold wrapping of a right-angled
isosceles triangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14033 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Optimal Twisted Paper Cylinder Montgomery, Noah Schwartz, Richard Evan Metric Geometry An embedded twisted paper cylinder of aspect ratio $λ$ is a smooth isometric embedding of a flat $λ\times 1$ cylinder into $\R^3$ such that the images of the boundary components are linked. We prove that for such an object to exist we must have $λ>2$ and that this bound is sharp. We also show that any sequence of examples having aspect ratio converging to $2$ must converge to a (non-smooth) $4$-fold wrapping of a right-angled isosceles triangle. |
| title | The Optimal Twisted Paper Cylinder |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2309.14033 |