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
--This text refers to an out of print or unavailable edition of this title.
"Amazingly understandable ... After reading it twice, I still pick it up and scan it ... this book belongs in every mathematical library." ---- Charles Ashbacher, Book Reviews Editor, Journal of Recreational Mathematics
"Throughout the book there are lots of exercises of various degrees of difficulty. Many 'unsolved questions' provide opportunity for further research. I liked reading this book. ... well written, enjoyable to read, and very accessible." ---- Zentralblatt MATH
"I thought the book was very well suited for an undergraduate knot theory/ topology course. The exposition was very clear." ---- Jennifer Taback, Bowdoin College