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Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb{R}^3$
 
Edited by: Jorge Alberto Calvo North Dakota State University, Fargo, ND
Kenneth C. Millett University of California, Santa Barbara, CA
Eric J. Rawdon Duquesne University, Pittsburgh, PA
Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3
Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3
eBook ISBN:  978-0-8218-7894-1
Product Code:  CONM/304.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3
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Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3
Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb{R}^3$
Edited by: Jorge Alberto Calvo North Dakota State University, Fargo, ND
Kenneth C. Millett University of California, Santa Barbara, CA
Eric J. Rawdon Duquesne University, Pittsburgh, PA
eBook ISBN:  978-0-8218-7894-1
Product Code:  CONM/304.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3042002; 340 pp
    MSC: Primary 57; 49; 53; 82; 92; 52; 74;

    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.

    Readership

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

  • Table of Contents
     
     
    • Articles
    • Jonathan Simon - Physical knots [ MR 1953008 ]
    • Richard Randell - The space of piecewise-linear knots [ MR 1953009 ]
    • Jorge Alberto Calvo - Characterizing polygons in $\Bbb R^3$ [ MR 1953010 ]
    • Eric J. Rawdon and Robert G. Scharein - Upper bounds for equilateral stick numbers [ MR 1953011 ]
    • Kenneth C. Millett - An investigation of equilateral knot spaces and ideal physical knot configurations [ MR 1953012 ]
    • Tetsuo Deguchi and Miyuki K. Shimamura - Topological effects on the average size of random knots [ MR 1953333 ]
    • Akos Dobay, Pierre-Edouard Sottas, Jacques Dubochet and Andrzej Stasiak - Bringing an order into random knots [ MR 1953334 ]
    • E. J. Janse van Rensburg - The probability of knotting in lattice polygons [ MR 1953335 ]
    • E. J. Janse van Rensburg - Knotting in adsorbing lattice polygons [ MR 1953336 ]
    • Piotr Pieranski and Sylwester Przybyl - In search of the ideal trefoil knot [ MR 1953337 ]
    • Yuanan Diao and Claus Ernst - The crossing numbers of thick knots and links [ MR 1953338 ]
    • Rob Kusner - On thickness and packing density for knots and links [ MR 1953339 ]
    • John M. Sullivan - Approximating ropelength by energy functions [ MR 1953340 ]
    • R. Langevin and J. O’Hara - Conformal geometric viewpoints for knots and links. I [ MR 1953341 ]
    • O. Gonzalez, J. H. Maddocks and J. Smutny - Curves, circles, and spheres [ MR 1953342 ]
    • Giovanni Dietler, Piotr Pieranski, Sandor Kasas and Andrzej Stasiak - The rupture of knotted strings under tension [ MR 1953343 ]
    • Louis H. Kauffman and Sofia Lambropoulou - Classifying and applying rational knots and rational tangles [ MR 1953344 ]
    • Dennis Roseman - Untangling some spheres in $\mathbf {R}^4$ by energy minimizing flow [ MR 1953345 ]
    • Michael Soss and Godfried T. Toussaint - Convexifying polygons in 3D: a survey [ MR 1953346 ]
    • Robert Connelly, Erik D. Demaine and Günter Rote - Infinitesimally locked self-touching linkages with applications to locked trees [ MR 1953347 ]
    • Louis H. Kauffman - Biologic [ MR 1953348 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3042002; 340 pp
MSC: Primary 57; 49; 53; 82; 92; 52; 74;

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.

Readership

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

  • Articles
  • Jonathan Simon - Physical knots [ MR 1953008 ]
  • Richard Randell - The space of piecewise-linear knots [ MR 1953009 ]
  • Jorge Alberto Calvo - Characterizing polygons in $\Bbb R^3$ [ MR 1953010 ]
  • Eric J. Rawdon and Robert G. Scharein - Upper bounds for equilateral stick numbers [ MR 1953011 ]
  • Kenneth C. Millett - An investigation of equilateral knot spaces and ideal physical knot configurations [ MR 1953012 ]
  • Tetsuo Deguchi and Miyuki K. Shimamura - Topological effects on the average size of random knots [ MR 1953333 ]
  • Akos Dobay, Pierre-Edouard Sottas, Jacques Dubochet and Andrzej Stasiak - Bringing an order into random knots [ MR 1953334 ]
  • E. J. Janse van Rensburg - The probability of knotting in lattice polygons [ MR 1953335 ]
  • E. J. Janse van Rensburg - Knotting in adsorbing lattice polygons [ MR 1953336 ]
  • Piotr Pieranski and Sylwester Przybyl - In search of the ideal trefoil knot [ MR 1953337 ]
  • Yuanan Diao and Claus Ernst - The crossing numbers of thick knots and links [ MR 1953338 ]
  • Rob Kusner - On thickness and packing density for knots and links [ MR 1953339 ]
  • John M. Sullivan - Approximating ropelength by energy functions [ MR 1953340 ]
  • R. Langevin and J. O’Hara - Conformal geometric viewpoints for knots and links. I [ MR 1953341 ]
  • O. Gonzalez, J. H. Maddocks and J. Smutny - Curves, circles, and spheres [ MR 1953342 ]
  • Giovanni Dietler, Piotr Pieranski, Sandor Kasas and Andrzej Stasiak - The rupture of knotted strings under tension [ MR 1953343 ]
  • Louis H. Kauffman and Sofia Lambropoulou - Classifying and applying rational knots and rational tangles [ MR 1953344 ]
  • Dennis Roseman - Untangling some spheres in $\mathbf {R}^4$ by energy minimizing flow [ MR 1953345 ]
  • Michael Soss and Godfried T. Toussaint - Convexifying polygons in 3D: a survey [ MR 1953346 ]
  • Robert Connelly, Erik D. Demaine and Günter Rote - Infinitesimally locked self-touching linkages with applications to locked trees [ MR 1953347 ]
  • Louis H. Kauffman - Biologic [ MR 1953348 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.