On sphere-filling ropes
Geometric Topology
2014-01-29 v1
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.
Cite
@article{arxiv.1005.4609,
title = {On sphere-filling ropes},
author = {Henryk Gerlach and Heiko von der Mosel},
journal= {arXiv preprint arXiv:1005.4609},
year = {2014}
}
Comments
15 pages, 8 figures