Self-contact Sets for 50 Tightly Knotted and Linked Tubes
| dc.creator | Ashton, Ted | |
| dc.creator | Cantarella, Jason | |
| dc.creator | Piatek, Michael | |
| dc.creator | Rawdon, Eric | |
| dc.date | 2005-08-15 | |
| dc.date.accessioned | 2026-07-07T05:22:22Z | |
| dc.date.available | 2026-07-07T05:22:22Z | |
| dc.description | 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. | |
| dc.description | 26 pages, 53 figures, for higher-resolution images, see http://www.cs.washington.edu/homes/piatek/contact_table/ | |
| dc.identifier | https://arxiv.org/abs/math/0508248 | |
| dc.identifier | http://arxiv.org/abs/math/0508248 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76033 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53-04 (Primary) 65D18, 53A04 (Secondary) | |
| dc.title | Self-contact Sets for 50 Tightly Knotted and Linked Tubes | |
| dc.type | text |