Curvature and torsion of the tight closed trefoil knot

Fourier Approximation of Symmetric Ideal Knots

“…The three ellipsoid ended axis give the second symmetry, which is a rotation of angle π. The generators of the symmetry group are one element of both types[4].1250057-7 J. Knot Theory Ramifications 2012.21.…”

High resolution portrait of the ideal trefoil knot

“…The curvature achieves indeed its upper limit value, but this happens not at six distinct points, but on six finite intervals. The speculation formulated by Carlen et al concerning torsion of the ideal knot does not find in the analysis performed by Baranska et al neither confirmation nor contradiction [13]. The torsion data proved to be also very noisy.…”

“…15 in ref. [13], where the curvature of the N = 3552 knot in the region of one of the double peaks, the first conjecture formulated by Carlen et al is too weak. The curvature achieves indeed its upper limit value, but this happens not at six distinct points, but on six finite intervals.…”

“…Results of the pursuit for the determination of the ropelength of the ideal trefoil knot are gathered in table I. [12] and [13] were found by Przybyl. Ropelength values marked with a question marked were calculated with a method that was not clearly specified.…”

“…[10] can be confronted with results of an analysis performed by Baranska et al [13]. The knot analyzed by the authors contained N = 3550 vertices.…”