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Search Home : Science : Math : Topology : Knot Theory
See Also:
- Knots on the Web (Peter Suber): 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.
- BraidLink: Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots 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: An overview of knot theory from Mathworld
- Knot Theory Group University of Liverpool: Links to preprints and to programs written in pascal for doing knot calculations.
- Knot Theory Invariants: The HOMFLY Polynomial: A brief article on the HOMFLY polynomial and how it is calculated.
- Knot Theory Online: This site is designed for mathematics students at the high school and college levels as an introduction to an area of mathematics seldom explored in the typical math classroom - the Theory of Knots.
- 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 Tie''.
- 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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