Knot Theory (Topology)

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Knot Theory Sites:

Thomas Fink (Tie Knots) 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 (Knot Theory) http://www.tcm.phy.cam.ac.uk/~tmf20/ Using Topology to Probe the Hidden Action of Enzymes 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). (Knot Theory) http://www.ams.org/notices/199505/sumners.pdf Knot Theory Online 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. (Knot Theory) http://www.freelearning.com/knots/ Geometry and the Imagination Geometry and the Imagination: Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology. (Knot Theory) http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html A Third Year Lecture Course on Knots 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. (Knot Theory) http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html BraidLink BraidLink: Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids. (Knot Theory) http://www.knot-theory.org/ Knot Theory Invariants: The HOMFLY Polynomial Knot Theory Invariants: The HOMFLY Polynomial: A brief article on the HOMFLY polynomial and how it is calculated. (Knot Theory) http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html The KnotPlot Site 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. (Knot Theory) http://www.cs.ubc.ca/labs/imager/contributions/scharein/KnotPlot.html Knotscape Knotscape: By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris. (Knot Theory) http://www.math.utk.edu/~morwen/knotscape.html A Circular History of Knot Theory 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. (Knot Theory) http://www.math.buffalo.edu/~menasco/Knottheory.html Knot Theory Group University of Liverpool Knot Theory Group University of Liverpool: Links to preprints and to programs written in pascal for doing knot calculations. (Knot Theory) http://www.liv.ac.uk/PureMaths/MIN_SET/CONTENT/RESEARCH_GROUPS/knots.html Harmonic Knots Harmonic Knots: An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings. (Knot Theory) http://www.carthage.edu/~trautwn/ Knot Plot 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) http://www.pims.math.ca/knotplot/ Kauffman, Louis H 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 Theory) http://bilbo.math.uic.edu/~kauffman/ Morwen Thistlethwaite's Home Page 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. (Knot Theory) http://www.math.utk.edu/~morwen/ A Knot Theory Primer 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. (Knot Theory) http://www.inst.bnl.gov/~wei/contents.html String Figure Mathematics (or Trivial Knot Theory) 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. (Knot Theory) http://website.lineone.net/~m.p/sf/menu.html Cook's Borromean Ring Links 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. (Knot Theory) http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.html Pictures of Knots Pictures of Knots: A table of graphics of all knots of up to nine crossings. Also includes pictures of some links. (Knot Theory) http://www.math.unl.edu/~mbritten/ldt/table9.gif The Geometry Junkyard: Knot Theory The Geometry Junkyard: Knot Theory: A page of links on geometric questions arising from knot embeddings. (Knot Theory) http://www.ics.uci.edu/~eppstein/junkyard/knot.html New Knot Tables New Knot Tables: Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos. (Knot Theory) http://members.tripod.com/vismath7/knotab/ History of Knot Theory 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. (Knot Theory) http://www.maths.ed.ac.uk/~aar/knots/index.htm Megamath Knot Theory Page Megamath Knot Theory Page: An introductory overview of knot theory. (Knot Theory) http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html Knots on the Web (Peter Suber) 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. (Knot Theory) http://www.earlham.edu/~peters/knotlink.htm Mathematics and Knots Exhibition Mathematics and Knots Exhibition: High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory. (Knot Theory) http://www.bangor.ac.uk/cpm/exhib/ The Knot Theory Home Page The Knot Theory Home Page: Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations. (Knot Theory) http://library.thinkquest.org/12295/main.html Knot Theory Knot Theory: Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations. (Knot Theory) http://www.mapleapps.com/categories/mathematics/Knot%20theory/html/Knots.htm