Quadrisecants give new lower bounds for the ropelength of a knot
  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. 
Elizabeth Denne, Yuanan Diao, John M Sullivan