2005/08/15 by Ted Ashton, Jason Cantarella, Ashton, Ted +5
Mathematics · #53-04 (Primary) 65D18 #53A04 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53-04 #msc:53A04 #msc:65D18
paper · pdf · doi:10.48550/arxiv.math/0508248
26 pages, 53 figures, for higher-resolution images, see http://www.cs.washington.edu/homes/piatek/contact_table/
arxiv created 2005/08/15 · arxiv updated 2009/12/01
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.