The Optimal Twisted Paper Cylinder
| Autor: | Schwartz, Richard Evan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A smooth twisted paper cylinder of aspect ratio $\lambda$ is an isometric embedding of a $1 \times \lambda$ cylinder into $\pmb{R}^3$ such that the images of the boundary components are linked. We prove that for such an object to exist we must have $\lambda>2$ and that this bound is sharp. We also show that any sequence of examples having aspect ratio converging to $2$ must converge, up to isometries, to a certain $4$-fold wrapping of a right-angled isosceles triangle. Comment: This paper is a sequel to my paper about the optimal paper Moebius band, arXiv:2308.12641. This version is the same as the previous one except that (1) I correct a misstatement about the uniqueness of the right isosceles cylinder and (2) I mention the connection to folded ribbon knots |
| Databáze: | arXiv |
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