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.
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.