Work

Quadrisecants give new lower bounds for the ropelength of a knot

Year: 2006

Type: article

Abstract: Using the existence of a special 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 16.372, so our new bounds are quite sharp.

Source: Geometry & Topology

DOI: 10.2140/gt.2006.10.1

Authors: Elizabeth Denne, Yuanan Diao, John M Sullivan

Institutions: Harvard University, University of North Carolina at Charlotte, Technische Universität Berlin

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, University of Illinois at Urbana-Champaign

Awards: Computation of Rope Length of Large Thick Knots, Optimal Geometry: Theory and Computation