# Symmetric Bends: How to Join Two Lengths of Cord

World Scientific, 1995 - Electronic books - 163 pages
A bend is a knot securely joining together two lengths of cord (or string or rope), thereby yielding a single longer length. There are many possible different bends, and a natural question that has probably occurred to many is: OC Is there a OCybestOCO bend and, if so, what is it?OCOMost of the well-known bends happen to be symmetric OCo that is, the two constituent cords within the bend have the same geometric shape and size, and interrelationship with the other. Such OCysymmetric bendsOCO have great beauty, especially when the two cords bear different colours. Moreover, they have the practical advantage of being easier to tie (with less chance of error), and of probably being stronger, since neither end is the weaker.This book presents a mathematical theory of symmetric bends, together with a simple explanation of how such bends may be invented. Also discussed are the additionally symmetric OCytriply symmetricOCO bends. Full details, including beautiful colour pictures, are given of the OCybest 60OCO known symmetric bends, many of which were created by these methods of invention.This work will appeal to many OCo mathematicians as well as non-mathematicians interested in beautiful and useful knots."

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### Contents

 Chapter 1 INTRODUCTION SUMMARY 1 THE ELEMENTARY SYMMETRIC BENDS 9 GEOMETRY PLANAR REPRESENTATIONS 17 Chapter 4 TOPOLOGICAL CONSIDERATIONS AND A THEOREM 29 Chapter 5 PRACTICAL CONSIDERATIONS TRIPLE SYMMETRY 49 SIXTY SYMMETRIC BENDS 67
 Chapter 7 MISCELLANY 135 Chapter 8 HOW TO INVENT SYMMETRIC BENDS 143 Appendix 157 Bibliography 159 Index 161 Copyright