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Knot Theory
Websites
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.
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A powerful invariant of unoriented links A program for computing Seifert matrices M457 Web Page Some pedagogical 3D images Puzzle: identify this knot....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.
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The KnotPlot Site Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four...The most comprehensive collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books.
http://www.earlham.edu/~peters/knotlink.htm
Includes examples, solutions, knot tables, pretty pictures. Course material includes: colouring, Alexander and Jones polynomials, tangles and braids.
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The Knot Theory MA3F2 page Little more than linear algebra plus an ability to visualise objects in 3-dimensions. Some knowledge of groups given by generators and relations, and some basic topology would be helpful. The lectures and mind map that follow (from 2004) will be...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.
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1 In the nineteenth century physicists were speculating about the underlying principles of atoms. In 1867, Lord Kelvin put forward a comprehensive theory of atoms which, through heuristic reasoning, seemed to explain several of the essential qualities of the chemical elements....High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory.
http://www.bangor.ac.uk/cpm/exhib/
Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids.
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Patrick Bangert Patrick Bangert...Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson.
http://www.maths.ed.ac.uk/~aar/knots/index.htm
Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format).
http://www.ams.org/notices/199505/sumners.pdf
Comprehensive knot theory site focusing on the knot classification problem and knot tabulations. Has a tabulation of knots with up to 12 crossings.
http://www.inst.bnl.gov/~wei/contents.html
A page of links on geometric questions arising from knot embeddings.
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The Geometry Junkyard: Knot Theory There is of course an enormous body of work on knot invariants, the 3-manifold topology of knot complements, connections between knot theory and statistical mechanics, etc. I am instead interested here primarily in geometric questions arising from knot embeddings. Animated...Links to preprints and to programs written in pascal for doing knot calculations.
http://www.liv.ac.uk/PureMaths/M...NTENT/RESEARCH_GROUPS/knots.html
An introduction to harmonic knots. Gives (parametric) formulas for knots of up to 7 crossings.
http://www.carthage.edu/~trautwn/
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.
http://bilbo.math.uic.edu/~kauffman/
A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.
http://www.math.unl.edu/~mbritten/ldt/table9.gif
Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
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Geometry and the Imagination Thron has called attention to the following passage from The Adventure of the Priory School, by Sir Arthur Conan Doyle This track, as you perceive, was made by a rider who was going from the direction of the school Or...An introductory overview of knot theory.
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Ideas, Concepts and Definitions Theory is the mathematical study of knots. A mathematical knot has no loose or dangling ends; the ends are joined to form a single twisted loop. The central problem of knot theory is distinguishing between various knots and classifying them....By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.
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Document Title These are binary versions of release 1.01 of Knotscape. Please see the README file for details of what's new. README Download Knotscape 1.01 (Linux binaries, compatible with Redhat 7.x 4729966 bytes) Download Knotscape 1.01 (SUN4 binaries, not compatible with the...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.
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The KnotPlot Site Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four...Links to pages and two outlines of proofs that show the Borromean rings can't be made from circular rings.
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Cook's Borromean Ring Links Here are some links to pages about Borromean rings. This is not intended to be a complete list people are apparently rather industrious by nature, at least when it comes to Borromean rings, and they seem to have been getting...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''.
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Thomas M. Fink Thomas M. Fink...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.
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Knot Theory Online The Web Site for Learning More about Mathematical Knot Theory Here you can learn about a different kind of Mathematics! Links on this site HOME HISTORY INTRO ADVANCED KT TODAY ACTIVITIES FUN] KT HOME Main Page KT HISTORY History of Knot Theory INTRO TO KNOTS What are knots? ADVANCED KT...An overview of knot theory from Mathworld
http://mathworld.wolfram.com/topics/KnotTheory.html
Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.
http://www.mapleapps.com/categor...ics/Knot%20theory/html/Knots.htm
Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.
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NEW KNOT TABLES New knot tables based on the notion of knot families are given. Using the methods of experimental mathematics, particular results obtained for knots with n 19 crossings belonging to the families p, pq, p1q, p11q, p111q, pqr, pq1r are extended,...Introductory level tutorial requiring only a high school mathematics background, some linear algebra is needed in places.
http://www.yucc.yorku.ca/~mouse/knots/knots.html
Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.
http://library.thinkquest.org/12295/
A brief article on the HOMFLY polynomial and how it is calculated.
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Knot Theory Invariants: The HOMFLY Polynomial Polynomial excited the mathematical community to the point that new polynomial invariants were being created at a stupendous rate. One of the objectives of the time was to find a polynomial that generalized both the Alexander and Jones polynomial. The...