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.
Citation
Elizabeth Denne. Yuanan Diao. John M Sullivan. "Quadrisecants give new lower bounds for the ropelength of a knot." Geom. Topol. 10 (1) 1 - 26, 2006. https://doi.org/10.2140/gt.2006.10.1
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