Symmetric Bends: How to Join Two Lengths of Cord

Front Cover
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
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