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.

Knots are well known as symbols of moral relationships. This book develops an exciting new view of this otherwise taken-for-granted image and considers their metaphoric value in and for moral order. In chapters that focus on Japan, China, Europe, South America and in several Pacific Island societies, granular ethnography depicts how knots are deployed to express unity in daily and ritual embodiment, political authority and the cosmos, as well as in social thought. The volume will be of interest to anthropologists and other scholars concerned with metaphor and symbolism, material culture and technology.

Needlework serves functional purposes, such as providing warmth, but has also communicated individual and social identity, spiritual beliefs, and aesthetic ideals throughout time and geography. Needlework traditions are often associated with rituals and celebrations of life events. Often-overlooked by historians, practicing needlework and creating needlework objects provides insights to the history of everyday life. Needlework techniques traveled with merchants and explorers, creating a legacy of cross-cultural exchange. Some techniques are virtually universal and others are limited to a small geographical area. Settlers brought traditions which were sometimes re-invented as indigenous arts. This volume of approximately 75 entries is a comprehensive resource on techniques and cultural traditions for students, information professionals, and collectors.

An introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics.

All knots are useful, but many can also be very beautiful. Here, Lindsey Philpott, expert knot tyer, sets out to provide the most comprehensive, useful, and attractive book of decorative knots from around the world. Readers will learn the materials, methods, measurements, and tools needed to tie dozens of beautiful knots. Flat knots, round knots, square knots, covering knots—you name it, and this book has it. From braids to plaits to sinnets, here are step-by-step instructions accompanied by full-color photographs for the knot tyer’s reference. Chapters include: Getting Started Purely Decorative Knots Netting and Woven Knots Turk’s Head Knots Knob Knots And much more! Philpott provides a brief history of knotting, in addition to instructions and helpful images. Practical tips, like what materials not to use will advise beginners about the details of knot tying. Once you practice the knots illustrated in these pages, you can use the information to create your own individual style—and even some new knots! Handy reference book as well as a beautiful gift, this is an essential addition to every knot enthusiast’s library.

LinKnot — Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.

The collection of papers forming this volume is intended to provide a deeper study of some mathematical and physical subjects which are at the core of recent developments in the natural and living sciences. The book explores some far-reaching interfaces where mathematics, theoretical physics, and natural sciences seem to interact profoundly. The main goal is to show that an accomplished movement of geometrisation has enabled the discovery of a great variety of amazing structures and behaviors in physical reality and in living matter. The diverse group of expert mathematicians, physicists and natural scientists present numerous new results and original ideas, methods and techniques. Both academic and interdisciplinary, the book investigates a number of important connections between mathematics, theoretical physics and natural sciences including biology.

One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.

The book describes current research into all aspects of craftwork in ancient Egypt.