Title

Approximating smooth thickness

Department/School

Mathematics

Date

2-1-2000

Document Type

Article

Keywords

Knots, Polygonal Knots, Thickness, Ropelength, Knot Energies

Abstract

The thickness of a knot is the radius of the thickest rope with which the knot could be tied. Basic properties of thickness have been established. However, thickness is difficult to compute for all but a few knot conformations. Thus, a continuous polygonal thickness function is needed to approximate its smooth analogue. The most natural definition yields incorrect estimates on a planar circle. Here, a polygonal thickness function is defined and shown to be continuous and to correctly approximate smooth thickness with an elementary inscribing algorithm. Examples of thickness estimations are also given.

Volume

9

Issue

1

Published in

Journal of Knot Theory and Its Ramifications

Citation/Other Information

Rawdon, E.J. (2000). Approximating smooth thickness, Journal of Knot Theory and Its Ramifications 9(1). 113–145. https://doi.org/10.1142/S0218216500000062.

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