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Knot Theory
- The most comprehensive collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books.|
» A Circular History of Knot Theory - Starting with the flawed theory of Kelvin's knotted vortex to the work of Thurston, Jones and Witten, knot theory has circled back to its ancestral origins of theoretical physics.
» A Knot Theory Primer - Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
» A Third Year Lecture Course on Knots - Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
» Cook's Borromean Ring Links - Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
» Geometry and the Imagination - Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
» Harmonic Knots - An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
» History of Knot Theory - Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
» Kauffman, Louis H - A topologist working in knot theory discusses the connection between knot theory and statistical mechanics. Sections on cybernetics and knots, Fourier knots and the author's research papers.
» Knot Plot - A collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a program to visualize and manipulate mathematical knots in three and four dimensions.
» Knot Theory - Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
» Knot Theory Invariants: The HOMFLY Polynomial - A brief article on the HOMFLY polynomial and how it is calculated.
» Knotscape - By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
» Mathematics and Knots Exhibition - High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
» Megamath Knot Theory Page - An introductory overview of knot theory.
» Morwen Thistlethwaite's Home Page - Has many beautiful images of symmetric knots, and information about a computer program called Knotscape (compiled binaries for Linux, Sunos and Alpha platforms). Includes pictures of knots with 13 crossings or less.
» New Knot Tables - Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
» Pictures of Knots  - A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
» String Figure Mathematics (or Trivial Knot Theory) - A mathematical analysis of string figures. Theorems, examples, illustrations and conjectures on patterns created with an unknotted string.
» The Geometry Junkyard: Knot Theory - A page of links on geometric questions arising from knot embeddings.
» The Knot Theory Home Page - Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
» The KnotPlot Site - Has a large number of beautiful graphics of knots created with KnotPlot. Contains an introductory section on mathematical knot theory. KnotPlot software for various platfroms can be downloaded.
» Thomas Fink (Tie Knots) - Thomas Fink and Yong Mao, used ideas from statistical mechanics to show there are 85 ways to tie a tie. They discovered a number of new aesthetically pleasing tie knots. This page has links to their original papers and to their book ``The 85 Ways to Tie a
» Using Topology to Probe the Hidden Action of Enzymes - Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format).
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Last Updated: 2007-04-24 09:54:10
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