Symmetric Bends How To Join Two Lengths Of Cord

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."

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: “Is there a ‘best’ bend and, if so, what is it?” Most of the well-known bends happen to be symmetric — that is, the two constituent cords within the bend have the same geometric shape and size, and interrelationship with the other. Such ‘symmetric bends’ 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 ‘triply symmetric’ bends. Full details, including beautiful colour pictures, are given of the ‘best 60’ known symmetric bends, many of which were created by these methods of invention. This work will appeal to many — mathematicians as well as non-mathematicians interested in beautiful and useful knots. Contents:Sufficiency: The Elementary Symmetric BendsNecessity: Geometry and Planar RepresentationsTopological Considerations and a TheoremPractical Considerations and Triple SymmetrySixty Symmetric Bends (Includes 16-page colour section)MiscellanyHow to Invent Symmetric Bends Readership: Mathematicians and general readers interested in knots. keywords:Geometry;Symmetry;Mirror Image;Congruency;Orthogonality;Practical Knots;Symmetric Bend;Symmetric Knot Diagram;Knot Invention;Splice;Loop;Hitch

This book discusses the origins of ornamental art -- illustrated by the oldest examples, dating mostly from the paleolithic and neolithic ages, and considered from the theory-of-symmetry point of view. Because of its multidisciplinary nature, it will interest a wide range of readers: mathematicians, artists, art historians, architects, psychologists, and anthropologists. The book represents the complete analysis of plane symmetry structures, so it can be used by artists as a guide to the creation of new symmetry patterns. Some parts of the contents (such as Chapter 4, about conformal symmetry, and Chapter 6, about modularity in art) give the reader an opportunity to develop computer programs for producing images illustrating the corresponding symmetry forms.

This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (107).