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arXiv · 2309.14033

The Optimal Twisted Paper Cylinder

Noah Montgomery·Richard Evan Schwartz
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Abstract

An embedded twisted paper cylinder of aspect ratio $\lambda$ is a smooth isometric embedding of a flat $\lambda \times 1$ 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 $\lambda>2$ 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.

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Noah Montgomery, Richard Evan Schwartz. 2023-09-25. The Optimal Twisted Paper Cylinder. https://arxiv.org/abs/2309.14033

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