Self-contact Sets for 50 Tightly Knotted and Linked Tubes
Differential Geometry
2007-05-23 v1
Abstract
We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the trefoil and figure eight knots by simulated annealing -- we use constrained gradient-descent to provide new self-contact sets for those and 48 other knot and link types. The minimum length of all unit diameter tubes in a given knot or link type is called the ropelength of that class of curves. Our computations yield improved upper bounds for the ropelength of all knots and links with 9 or fewer crossings except the trefoil.
Keywords
Cite
@article{arxiv.math/0508248,
title = {Self-contact Sets for 50 Tightly Knotted and Linked Tubes},
author = {Ted Ashton and Jason Cantarella and Michael Piatek and Eric Rawdon},
journal= {arXiv preprint arXiv:math/0508248},
year = {2007}
}
Comments
26 pages, 53 figures, for higher-resolution images, see http://www.cs.washington.edu/homes/piatek/contact_table/