On sphere-filling ropes

Details On sphere-filling ropes On sphere-filling ropes

2010-05-25

arxiv.org/abs/1005.4609v1

Mathematics

Geometric Topology

15 pages, 8 figures

Scientific paper

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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