On sphere-filling ropes

Henryk Gerlach; Heiko von der Mosel

doi:10.4169/amer.math.monthly.118.10.863

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arXiv · 1005.4609

On sphere-filling ropes

Henryk Gerlach·Heiko von der Mosel

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Abstract

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered phases of long elastic rods stuffed into spherical shells.

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Henryk Gerlach, Heiko von der Mosel. 2010-05-25. On sphere-filling ropes. https://doi.org/10.4169/amer.math.monthly.118.10.863

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