High resolution portrait of the ideal trefoil knot

Abstract

The shape of the most tight trefoil knot with N=200640 vertices found with an appropriately modified finite element method is analyzed. The high number of vertices makes plots of its curvature and torsion very precise what allows the authors to formulate new, firmly justified conjectures concerning the shape of the ideal trefoil knot.

14 figures

References in corpus (2)

• Knot Tightening By Constrained Gradient Descent
• The Shapes of Tight Composite Knots

Cited by in corpus (2)

• The shapes of physical trefoil knots
• The Ropelength of Complex Knots