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Summary: Energy, ropelength, and other physical
aspects of equilateral knots
Kenneth C. Millett
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93016 USA
Email: millett@math.ucsb.edu
Eric J. Rawdon
Department of Mathematics and Computing
Chatham College
Pittsburgh, PA 15232 USA
http://monkey.chatham.edu/rawdon
Email: rawdon@chatham.edu
Abstract
Equilateral spatial polygons provide useful models of spatial knots and the spaces of
such knots. Associated to these con gurations are energies, ropelength or thickness,
crossing number, writhe, and other measures re
ecting the spatial structure such as
the volume and surface area on the convex hull. The optimization of the energy and
the ropelength and physical and spatial characteristics of optimized con gurations
are the subject of this paper. Data from computer explorations of these facets of
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