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arXiv · 2010.15204

Shortest closed curve to inspect a sphere

Mohammad Ghomi·James Wenk
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Abstract

We show that in Euclidean 3-space any closed curve which lies outside the unit sphere and contains the sphere within its convex hull has length at least $4π$. Equality holds only when the curve is composed of $4$ semicircles of length $π$, arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.

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Mohammad Ghomi, James Wenk. 2021-07-21. Shortest closed curve to inspect a sphere. https://arxiv.org/abs/2010.15204

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