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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 seam lines 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.
Corentin Jean Dominique Fivet, Nicolas Robin Montagne, Olivier Baverel
Corentin Jean Dominique Fivet, Nicolas Robin Montagne, Olivier Baverel
Mikhail Kapralov, Jakab Tardos