Title

Can computers discover ideal knots?

Department/School

Mathematics

Date

9-1-2003

Document Type

Article

Keywords

geometric knots, polygonal knots, ropelength

Abstract

We discuss the relationship between polygonal knot energies and smooth knot energies, concentrating on ropelength. We show that a smooth knot can be inscribed in a polygonal knot in such a way that the ropelength values are close. For a given knot type, we show that polygonal ropelength minima exist and that the minimal polygonal ropelengths converge to the minimal ropelength of the smooth knot type. A subsequence of these polygons converges to a smooth ropelength minimum. Thus, ropelength minimizations performed on polygonal knots do, in fact, approximate ropelength minimizations for smooth knots.

Volume

12

Issue

3

Published in

Experimental Mathematics

Citation/Other Information

Rawdon, E.J. (2003). Can computers discover ideal knots?, Experimental Mathematics, 12(3), 287-302, DOI: 10.1080/10586458.2003.10504499

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