Title

Ropelength of tight polygonal knots

Department/School

Mathematics

Date

1-1-2005

Document Type

Book Chapter

Keywords

ropelength, tight polygonal knots

Abstract

A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is shown. Two ways of calculating the ropelength of tight polygonal knots are compared. An analytical calculation performed for a model knot shows that an appropriately weighted average should provide a good estimation of the minimum ropelength for relatively small numbers of edges. Comment: 27 pages, to appear in "Physical and Numerical Models in Knot Theory and their Application to the Life Sciences"

Published in

Physical and Numerical Models in Knot Theory

Citation/Other Information

Baranski, J., Pierasnki, P. & Rawdon, E.J. (2005). Ropelength of tight polygonal knots. In Calvo, J. A., Millett, K. C., Rawdon, E. J., & Stasiak, A. (2005). Physical and numerical models in knot theory: including applications to the life sciences (Vol. 36). World Scientific Publishing Co. Pte. Ltd. https://doi.org/10.1142/9789812703460_0016.

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