In February 2001, scientists at the Department of Energy''s Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more than that, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.
A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, however, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere," a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer offers an engaging if challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable, or hyperbolic. As perhaps befits its subject, Adams''s prose is sometimes, well, tangled ("a knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing"), but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee
Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. "The Knot Book" is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. "The Knot Book" is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in "The Knot Book".Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer. Other key books of interest available from the "AMS" are "Knots and Links" and "The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes".
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