On sphere-filling ropes

• Published in 2010
• Added on 2012-10-29

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.

Links

• http://arxiv.org/abs/1005.4609
• http://arxiv.org/pdf/1005.4609v1

Other information

BibTeX entry

@article{Gerlach2010,
	key = {Gerlach2010},
	type = {article},
	title = {On sphere-filling ropes},
	author = {Gerlach, Henryk and von der Mosel, Heiko},
	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.},
	comment = {},
	date_added = {2012-10-29},
	date_published = {2010-05-01},
	urls = {http://arxiv.org/abs/1005.4609,http://arxiv.org/pdf/1005.4609v1},
	collections = {Easily explained,Geometry,Fun maths facts},
	archivePrefix = {arXiv},
	arxivId = {1005.4609},
	eprint = {1005.4609},
	journal = {Nature},
	month = {may},
	pages = 15,
	url = {http://arxiv.org/abs/1005.4609 http://arxiv.org/pdf/1005.4609v1},
	year = 2010,
	primaryClass = {math.GT},
	urldate = {2012-10-29}
}