Open Access
Translator Disclaimer
2003 Can Computers Discover Ideal Knots?
Eric J. Rawdon
Experiment. Math. 12(3): 287-302 (2003).

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.

Citation

Download Citation

Eric J. Rawdon. "Can Computers Discover Ideal Knots?." Experiment. Math. 12 (3) 287 - 302, 2003.

Information

Published: 2003
First available in Project Euclid: 15 June 2004

zbMATH: 1073.57003
MathSciNet: MR2034393

Subjects:
Primary: 57M25

Keywords: geometric knots , Polygonal knots , ropelength

Rights: Copyright © 2003 A K Peters, Ltd.

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.12 • No. 3 • 2003
Back to Top