 
Summary: 3/21/01
1
An Investigation of Polygonal Knot Spaces and Ideal Physical Knot Configurations
Kenneth C. Millett
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93103
USA
(millett@math.ucsb.edu)
Abstract
Spaces of polygonal knots, subject to specified constraints such as the number of
nondegenerate edges or the requirement of having fixed edge lengths, provide the context
within which it is appropriate to study configurations which are ideal with respect to a variety
of natural physically motivated constraints. Even for polygonal knots with relatively few
vertices, the high dimensionality and complexity of the knot space structure makes analytical
investigations impractical. In this note we will discuss the methods and the results of a
Monte Carlo investigation of several fundamental approaches to ideal polygonal knot
configurations for small numbers of edges.
Introduction
One goal of this note is the exploration of the global structure of knot space from the
