Quadrisecants give new lower bounds for the ropelength of a knot

By E. Denne, Y. Diao, John M. Sullivan Jr.. 2004

51 citations recorded by the source corpus.

Using the existence of a quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.34, so our new bounds are quite sharp.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b3531f3ea1c8eb8c3c54e9acb240e1dec9d9dc86