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History and Science of Knots by John Christopher Turner Pdf
In view of the explosion of mathematical theories of knots in the past decade, with consequential applications, this book sets down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device - the knot.
History and Science of Knots by J C Turner,P van de Griend Pdf
This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots. Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day. In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot. Contents:Prehistory and Antiquity:Pleistocene KnottingWhy Knot? — Some Speculations on the First KnotsOn Knots and Swamps — Knots in European PrehistoryAncient Egyptian Rope and KnotsNon-European Traditions:The Peruvian QuipuThe Art of Chinese Knots Works: A Short HistoryInuit KnotsWorking Knots:Knots at SeaA History of Life Support KnotsTowards a Science of Knots?:Studies on the Behaviour of KnotsA History of Topological Knot Theory of KnotsTramblesCrochet Work — History and Computer ApplicationsDecorative Knots and Other Aspects:The History of MacraméA History of LaceHeraldic KnotsOn the True Love Knotand other papers Readership: Mathematicians, archeologists, social historians and general readers. keywords:Antiquit;Braiding;Climbing;Heraldry;History;Knots;Lace;Mariners;Prehistory;Quipus;Science;Theory;Topology;Knotting, Pleistocene;Egyptian;Inuit;Chinese;Mountaineering, Topological Knot Theory;Knot Theories;Quipo Knot Mathematics;Knot Strength Efficiency;Heraldic;True Love;Crochet;Computer Aided Design;Trambles “… it is a veritable compendium of information about every aspects of knots, from their links with quantum theory to attempts to measure their strength when tying climbing ropes together … the huge scope of this book makes it one I have turned to many times, for many different purposes.” New Scientists “I enjoyed browsing through all the chapters. They contain material that a mathematician would not normally come across in his work.” The Mathematical Intelligencer
THE ASHLEY BOOK OF KNOTS by Clifford W. Ashley Pdf
What else needs to be said about knots? Almost 650 pages of incredible knowledge, presented in a truzly unique manner. This is not a book of knots, it is the BOOK OF KNOTS. Was muss noch über Knoten gesagt werden? Fast 650 Seiten unglaubliches Wissen, präsentiert in einer wahrhaft einzigartigen Weise. Dies ist kein Buch über Knoten, es ist das BUCH DER KNOTEN.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Inka khipus--spun and plied cords that record information through intricate patterns of knots and colors--constitute the only available primary sources on the Inka empire not mediated by the hands, minds, and motives of the conquering Europeans. As such, they offer direct insight into the worldview of the Inka--a view that differs from European thought as much as khipus differ from alphabetic writing, which the Inka did not possess. Scholars have spent decades attempting to decipher the Inka khipus, and Gary Urton has become the world's leading authority on these artifacts. In Inka History in Knots, Urton marshals a lifetime of study to offer a grand overview of the types of quantative information recorded in khipus and to show how these records can be used as primary sources for an Inka history of the empire that focuses on statistics, demography, and the "longue durée" social processes that characterize a civilization continuously adapting to and exploiting its environment. Whether the Inka khipu keepers were registering census data, recording tribute, or performing many other administrative tasks, Urton asserts that they were key players in the organization and control of subject populations throughout the empire and that khipu record-keeping vitally contributed to the emergence of political complexity in the Andes. This new view of the importance of khipus promises to fundamentally reorient our understanding of the development of the Inka state and the possibilities for writing its history.
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.
An Interactive Introduction to Knot Theory by Inga Johnson,Allison K. Henrich Pdf
This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.
Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book when tools from linear algebra and from basic group theory are introduced to study the properties of knots. Livingston guides readers through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics's most beautiful topics—symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject—the Conway, Jones, and Kauffman polynomials. A supplementary section presents the fundamental group which is a centerpiece of algebraic topology.
The ultimate visual guide to all types of knots. Avoid getting yourself into a tangle by following detailed step-by-step instructions that show you how to tie and untie more than 100 knots. Whichever knotty scenario you find yourself in, from in your own garden, to up in the mountains or across seas, this reference book will take you from novice to expert rope tier. Covering more than 100 knots for climbing, sailing, horse-riding, survival camping, and fishing as well as for gardening, DIY, medical, and even decorative purposes. The photographs of every step use strands of rope in different colors - so you can clearly see how to tie each knot. You’ll learn all about the fascinating stories behind how many of these knots were first tied as well as their original functions in this knot tying book. Each knot has simple to follow instructions on the features and benefits and what they can be used for. Includes knots such as figure-of-eights, reef knots, highwayman’s hitches, and monkey’s fists. Find out about techniques like sheer lashing and the constrictor knot. The book begins by teaching you all about rope materials and construction and how to maintain them. At the end of the book the glossary and index so you can easily find just the knot you’re in need of. There are more than 1,000 photographs, illustrations, and artworks. Expert author Des Pawson is a founding member of the International Guild of Knot Tyers. One-Stop Practical Guide to Tying and Using Knots Knots: The Complete Visual Guide is arranged by chapters covering Stopper Knots, Binding Knots, Bends, Hitches, Loops, Plaits & Sennits, and Splices & Whippings. It also includes detailed instructions for over 100 knots and fantastic beginner guides to help boy scouts, girl scouts, first-time climbers and everything in between become experienced campers, sailors, and mountaineers. Inside this visual guide, you’ll find: • Accessible text and tables that explain the features and benefits of each knot • Sequence spreads display the top five knots you need for a range of purposes, from sailing and fishing to gardening and gift-wrapping • Fun facts about the oldest knots and their history • Essential information on how to choose the best rope to use and how to maintain them More from DK Books: Don’t miss out on more fascinating visual reference books! Look for The Complete Sailing Manual, How to Garden, and The Survival Handbook from DK Books to build on your new-found knot skills.
Knot Theory and Its Applications by Kunio Murasugi Pdf
This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Lectures on Geometry by Edward Witten,Martin Bridson,Helmut Hofer,Marc Lackenby,Rahul Pandharipande Pdf
This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in an occasional series of volumes of CMI lectures. Although not explicitly linked, the topics in this inaugural volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.
Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this exciting new book that brings his findings and his passion for the subject to a more general audience. This beautifully illustrated comic book is appropriate for many mathematics courses at the undergraduate level such as liberal arts math, and topology. Additionally, the book could easily challenge high school students in math clubs or honors math courses and is perfect for the lay math enthusiast. Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle R. Adams uses the Tangle because "you can open it up, tie it in a knot and then close it up again." The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. Adams also presents a illustrative and engaging history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!
CLICK HERE TO DOWNLOAD A KNOT SAMPLER FROM THE CHAPTER ON "KNOTS FOR HIKING & CAMPING" (Provide us with a little information and we'll send your download directly to your inbox) * Guidelines for selecting the best rope and the best knot for the activity at hand * Knot-tying directions clearly illustrated with photos * New entry in the Mountaineers Outdoor Basics series It's fair to say that climber Clyde Soles is obsessed with ropes and knots and their absolute performance-since he regularly entrusts his life to ropes on sheer rock faces. His unique book explains how to select and use ropes, cordage, and webbing for the outdoors. Invaluable information is provided on rope handling techniques (how to avoid dreaded tangles) and the best methods for rope care and maintenance. Step-by-step directions for tying over 40 knots are clearly illustrated with photographs. Other useful features include a glossary and a knot comparison chart by activity. Chapters include Knots Basics (from Tripod Lashing to the Figure 8 Loop), Knots for Hikers and Climbers (from the Prusik knot to the Autoblock), Knots for Canoeists and Kayakers (from the Buntline hitch to the Bowline on a bight), and more. This is the definitive text on ropes and knots for anyone who plays in the outdoors!