**Contemporary Mathematics**

Volume: 304;
2002;
340 pp;
Softcover

MSC: Primary 57; 49; 53; 82; 92; 52; 74;

Print ISBN: 978-0-8218-3200-4

Product Code: CONM/304

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-7894-1
Product Code: CONM/304.E**

List Price: $105.00

Individual Member Price: $84.00

# Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb{R}^{3}$

Share this page *Edited by *
*Jorge Alberto Calvo; Kenneth C. Millett; Eric J. Rawdon*

The properties of knotted and linked configurations in space have long been of
interest to physicists and mathematicians. More recently and more widely, they
have become important to biologists, chemists, computer scientists, and
engineers. The depth and breadth of their applications are widely
appreciated. Nevertheless, fundamental and challenging questions remain to be
answered.

Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in
April 2001, this volume discusses critical questions and introduces new ideas
that will stimulate multi-disciplinary applications.

Some of the papers are primarily theoretical; others are experimental. Some are
purely mathematical; others deal with applications of mathematics to
theoretical computer science, engineering, physics, biology, or
chemistry. Connections are made between classical knot theory and the physical
world of macromolecules, such as DNA, geometric linkages, rope, and even cooked
spaghetti.

This book introduces the world of physical knot theory in all its
manifestations and points the way for new research. It is suitable for a
diverse audience of mathematicians, computer scientists, engineers, biologists,
chemists, and physicists.

#### Table of Contents

# Table of Contents

## Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb{R}^{3}$

- Contents v6 free
- Preface vii8 free
- Physical knots 114 free
- The space of piecewise-linear knots 3144
- Characterizing polygons in R3 3750
- Upper bounds for equilateral stick numbers 5568
- An investigation of equilateral knot spaces and ideal physical knot configurations 7790
- Topological effects on the average size of random knots 93106
- Bringing an order into random knots 115128
- The probability of knotting in lattice polygons 125138
- Knotting in adsorbing lattice polygons 137150
- In search of the ideal trefoil knot 153166
- The crossing numbers of thick knots and links 163176
- On thickness and packing density for knots and links 175188
- Approximating ropelength by energy functions 181194
- Conformal geometric viewpoints for knots and links I 187200
- Curves, circles, and spheres 195208
- The rupture of knotted strings under tension 217230
- Classifying and applying rational knots and rational tangles 223238
- Untangling some spheres in R4 by energy minimizing flow 261276
- Convexifying polygons in 3D: A survey 269284
- Infinitesimally locked self-touching linkages with applications to locked trees 287302
- Biologic 313328

#### Readership

Graduate students, mathematicians, computer scientists, engineers, biologists, chemists, and physicists.