On Sphere-Filling Ropes

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.


Published in:
American Mathematical Monthly, 118, 863-876
Year:
2011
Keywords:
Laboratories:




 Record created 2012-06-12, last modified 2018-03-17


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