1. Knot Theory Online - The Web Site For Learning More About Mathematical Knot Theo Welcome to KT (knot theory) Online! This Also, find out what is the central problem of knot theory and what properties knots have. This http://www.freelearning.com/knots/

Welcome to KT (Knot Theory) Online! Here you can learn about a different kind of Mathematics! Links on this site: [HOME] [HISTORY] [INTRO] [ADVANCED] ... KT HOME Main Page KT HISTORY History of Knot Theory INTRO TO KNOTS What are knots? ADVANCED KT Knot Theory in the Real World KT ACTIVITIES Online activities with knots for you to try KNOT FUNNY Interesting facts, knot-knot jokes, and knotty pictures... Welcome to KT (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. One thing that makes Knot Theory so interesting for mathematicians today is the fact that it's such a "new" topic - Knot Theory is a relatively young field with many opportunities for discovery and exploration by mathematicians young and old. Click below to jump to some of the topics you can learn about at KT Online: A Brief History of Knot Theory - From the mathematical surge of interest in knots a little over a century ago to the recent and exciting application of Knot Theory to DNA and synthetic chemistry, you can get an overview of why knots are such a fascination for scientists and mathematicians alike.

2. ThinkQuest : Library : Knot Theory Please email us your thoughts or sign our guestbook. knot theory. knot theory is a branch of topology that deals with knots and links. In topology, a sphere is the same as a cube, and a doughnut is http://library.thinkquest.org/12295/main.html

Index Math Knot Theory Who knew there was so much to know about mathematical knots? Featuring easy navigation and straightforward menus, this site explores the formulas and factoids associated with the study of topology. While advanced math students will benefit most, the site also includes a glossary and biographies of mathematicians and scientists, handy features for all types of students. Visit Site 1997 ThinkQuest Internet Challenge Languages English Students Jason B. Severn School, Severna Park, MD, United States Stefan Severn School, Severna Park, MD, United States Andrei Severn School, Severna Park, MD, United States Coaches Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Todd Severn School, Severna Park, MD, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

3. Ideas, Concepts And Definitions knot theory. knot theory is the mathematical study of knots. A mathematical knot play with them. Some important ideas in knot theory. http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html

Knot Theory Knot 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. The best way to learn about knots is to make some knots and play with them. Some important ideas in Knot Theory classifying knots knots as closed circular braids crossings keeping track of crossings ... seifert surfaces See also . . . Knot Coloring Puzzles A Table of Knots to Study and Make Untangling the Mathematics of Knots Knots, Links and Other Mathematical Tangles ... Knot Theory and the NCTM Standards

4. The Geometry Junkyard: Knot Theory There is of course an enormous body of work on knot invariants, the 3manifold topology of knot complements, connections between knot theory and statistical mechanics, etc. http://www.ics.uci.edu/~eppstein/junkyard/knot.html

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 3d curves and knots , Jos Leys. Atlas of oriented knots and links , Corinne Cerf extends previous lists of all small knots and links, to allow each component of the link to be marked by an orientation. Borromean rings don't exist . Geoff Mess relates a proof that the Borromean ring configuration (in which three loops are tangled together but no pair is linked) can not be formed out of circles. Dan Asimov discusses some related higher dimensional questions. Matthew Cook conjectures the converse Are Borromean links so rare? S. Javan relates the history of the links and describes various generalizations with more than three rings. For more history and symbolism of the Borromean rings, see Peter Cromwell's web site . See also Paul Bourke's Borromean rings page A Brunnian link . Cutting any one of five links allows the remaining four to be disconnected from each other, so this is in some sense a generalization of the Borromean rings. However since each pair of links crosses four times, it can't be drawn with circles.

5. Contents An Introduction to knot theory. Showing Knot Equivalence. Showing Knot Inequivalence. An Introduction to Braid Theory. The Knot Group. The "Color Tests http://www.inst.bnl.gov/~wei/contents.html

Table of Contents A Knot Theory Primer An Introduction to Knot Theory Showing Knot Equivalence Showing Knot Inequivalence ... Proving that the links cannot be decomposed This is the latest addition to this online tutorial. Its goal is to extend the discussion from the study of knots to the study of links You may be interested in my published book, The Mystery of Knots Charilaos Aneziris charilaos_aneziris@standardandpoors.com Educational institutions are encouraged to reproduce and distribute these materials for educational use free of charge as long as credit and notification are provided. For any other purpose except educational, such as commercial etc, use of these materials is prohibited without prior written permission.

6. Knots knot theory. by Rohit Chaudhary. knot theory is a mathematical study of knots. It is an area of mathematics known as topology. It is mainly used to distinguish between different types of knots and links. Looking at the history of knot theory, before people used to try to twist wires or threads http://www.mapleapps.com/categories/mathematics/Knot theory/html/Knots.htm

Knot Theory by Rohit Chaudhary Knot theory is a mathematical study of knots. It is an area of mathematics known as topology . It is mainly used to distinguish between different types of knots and links. There are some practical applications of knots that are discussed in more detail later. Looking at the history of Knot theory, before people used to try to twist wires or threads and try to classify different types of knots. Now a days, using the modern technology this can be done on the computer. The Knots shown in this page are all drawn using Maple software. Introduction - Introduction to Knot theory in more detail and some history behind it Description of Knot Theory - Describes the Knot Theory and some terms used Techniques of distinguishing knots - Different types of ways in which the knots can be distinguished Some types of Knots - Some types of Knots drawn using Maple and the worksheet Applications - Some applications of the Knot Theory and a link to the references Knots with their Conway Notations Some knots shown with their respective Conway Notations

7. 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. http://www.earlham.edu/~peters/knotlink.htm

Knots on the Web Artwork credits Unfortunately I'm much too busy with real, paying work nowadays to update Knots on the Web as often as I used to. Consequently, it has far too many dead links and omits far too many good, new sites. I wish I could say that this will change soon, but it won't. Until it does, please use what is still useful here and forgive the weak spots. If you have a specific knot need or question, and the surviving links here don't help you with it, then try posting your question to rec.crafts.knots or running a search on Google Welcome to my collection of knotting resources. My major sections are on Knot Tying Knot Theory , and Knot Art . But knot lovers will understand that these distinctions are artificial. For example, a good practical knot is both a nugget of hard-won technology and a thing of beauty. Decorative knotting can be useful, and in any case requires uncommon dexterity and practical tying ability. Software developed to help mathematical knot theorists has produced some of the most beautiful knot images ever seen. So look at all three sections even if you think your interests are narrow. You might become happily entangled. My fourth section is on Knot Discussion . Use these discussion forums to find answers to your knotting questions and to help others who know less than you do. My fifth section is on Knot Software . You'll be surprised at how knotting software can make it easier for you to learn to tie knots, to explore the mathematical properties of knots, and to create stunning images of knots, including knots never seen on Earth.

8. Mathematical Knots knot theory. Note another. The simplest form of knot theory involves the embedding of the unit circle into threedimensional space. http://www.cs.ubc.ca/nest/imager/contributions/scharein/knot-theory/knot-theory.

Knot theory Note: This page is part of the KnotPlot Site, where you'll find many more pictures of knots and links as well as MPEG animations and lots of things to download. Knot theory is a branch of algebraic topology where one studies what is known as the placement problem, or the embedding of one topological space into another. The simplest form of knot theory involves the embedding of the unit circle into three-dimensional space. For the purposes of this document a knot is defined to be a closed piecewise linear curve in three-dimensional Euclidean space R . Two or more knots together are called a link. Thus a mathematical knot is somewhat different from the usual idea of a knot, that is, a piece of string with free ends. The knots studied in knot theory are (almost) always considered to be closed loops. Two knots or links are considered equivalent if one can be smoothly deformed into the other, or equivalently, if there exists a homeomorphism on R which maps the image of the first knot onto the second. Cutting the knot or allowing it to pass through itself are not permitted. In general it is very difficult problem to decide if two given knots are equivalent, and much of knot theory is devoted to developing techniques to aid in answering this question. Knots that are equivalent to polygonal paths in three-dimensional space are called tame.

9. 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. http://www.math.buffalo.edu/~menasco/Knottheory.html

A Circular History of Knot Theory 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. Kelvin's theory conjectured that atoms were knotted tubes of ether. (To a topologist a knot in space is any closed loop having no self-intersections and a link is any collection of non-intersecting closed loops.) The topological stability and the variety of knots were thought to mirror the stability of matter and the variety of chemical elements. Kelvin's theory of vortex atoms was taken seriously for about two decades. Maxwell thought that ``it satisfies more of the conditions than any atom hitherto considers''. This theory inspired the celebrated Scottish physicist Peter Tait to undertake an extensive study and tabulation of knots in an attempt to understand when two knots were ``different''. (The later stages of this study were in collaboration with C. N. Little.) Tait's intuitive understanding of ``different'' and ``same'' is still a useful notion. Two knots are isotopic if one can be continuously manipulated in space (no self-intersections allowed) until it looks like the other. The accompanying

10. Journal Of Knot Theory And Its Ramifications (JKTR) Journal of knot theory and Its Ramifications intended as a forum for new developments in knot theory, particularly developments that create connections between http://www.worldscinet.com/jktr/jktr.shtml

What's New New Journals Browse Journals Search ... Mathematics Journal of Knot Theory and Its Ramifications (JKTR) This Journal is intended as a forum for new developments in knot theory, particularly developments that create connections between knot theory and other aspects of mathematics and natural science. The stance is interdisciplinary due to the nature of the subject. More Feature Articles (Free Online Sample Issue) Vol. 12, No. 7 (November 2003) Scharlemann-Thompson Untelescoping of Heegaard Splittings is Finer than Casson-Gordon's Tsuyoshi Kobayashi On the Reversibility of Twist-Spun Knots Cameron Mca. Gordon Ocneanu's Trace and Starkey's Rule Meinolf Geck and Nicolas Jacon Markov Theorem for Transversal Links S. Yu. Orevkov and V. V. Shevchishin A Large Complete Graph in a Space Contains a Link with Large Link Invariant Minori Shirai and Kouki Taniyama On the Classification of Rational 3-Tangles Hugo Cabrera-Ibarra Generalized Knot Complements and some Aspherical Ribbon Disc Complements Jens Harlander and Stephan Rosebrock On the Structure of Simply Represented Knots Frank J. Swenton

11. Knot Theory -- From MathWorld An overview of knot theory from Mathworld http://mathworld.wolfram.com/topics/KnotTheory.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Topology Knot Theory Braids General Knot Theory Knot Invariants Knot Operations ... Links

12. Knot-Theory.com - The Art And Science Of String Toys Searchable trick database with types, inventors, and descriptions of each trick. http://www.knot-theory.com

13. The Survival, Origin And Mathematics Of String Figures Trivial knot theory, history, and a few new designs by the author, Martin Probert. http://website.lineone.net/~m.p/sf/menu.html

The Survival, Origin and Mathematics of String Figures Includes a detailed inventory of over 1200 string figure artefacts in more than 20 museums worldwide, papers on "The British Museum A. C. Haddon String Figures", "The Origin of String Figures" and "String Figures and Knot Theory", and sixteen of the author's 21st-century string figures. by Martin Probert "the World's Most Widespread Game" (James Hornell, Discovery, NOTE: The text size on this website can be changed by the user. Please use your browser to adjust. 1) Museums and other institutions with string figure artefacts Begun 1999. Last revised April 2003 Museums and artefacts . An inventory of over 1200 string figure artefacts in more than 20 museums worldwide. The inventory includes string figures mounted on card, string figures on film, string figure photographs, and recordings of string figure songs. Holding institutions include the British Museum, the Harvard University Peabody Museum, the Australian Museum, and many others. "A wonderful project" Museum Archivist, North America (pers. comm.)

14. Knot-Theory.com - Those Who Can't Do, Theorize. Welcome to the knot theory Skill Toy Trick Library. Most Viewed 1. Dirty Bomb. 2. Kamikaze. 3. Cold Fusion. 4. Aluminum Whip. 5. And Whut? 6. Bermuda Triangle. http://www.knot-theory.com/tricklib/index.php

Welcome to the Knot Theory Skill Toy Trick Library Most Viewed: Dirty Bomb Kamikaze Cold Fusion Aluminum Whip ... Abundant Uranium This database serves as a central index for skill toy trick descriptions, illustrations, videos, and other information, contained both on this page and on others around the net. The main purpose is the spread information quickly and easily about tricks both old and new, to help new players learn, or experienced performers teach. Thanks to Spinwizard/Iconium for the initial trick list used to populate the DB. Thanks to tym.de/Jumper for the biggest yo-yo links page on the net, which we use for finding links. :) Thanks to diabolotricks.com for the initial diabolo trick information. Recently Updated: Cold Fusion Bermuda Triangle Barrel Rolls Breakaway ... Tidal Wave

15. Liverpool Pure Maths: Knot Theory Pure Mathematics knot theory. knot theory at Liverpool. Members of the Research Group. Hugh Morton (email morton@liv.ac.uk) Peter http://www.liv.ac.uk/PureMaths/MIN_SET/CONTENT/RESEARCH_GROUPS/knots.html

Pure Mathematics Knot Theory Dept. Home Page Find someone? Pure home page Knot Theory at Liverpool Members of the Research Group Hugh Morton (e-mail: morton@liv.ac.uk Peter Cromwell (e-mail: spmr02@liv.ac.uk Victor Goryunov (e-mail: goryunov@liv.ac.uk Elisabetta Beltrami (e-mail: elisa@liv.ac.uk or beltrami@gauss.dm.unipi.it Pedro Manchon (e-mail: pmanchon@liv.ac.uk Research Students Sascha Lukac (e-mail: lukac@liv.ac.uk Richard Hadji (e-mail: rhadji@liv.ac.uk Previous Members Anna Aiston Yongju Bae (e-mail: ybae@knu.ac.kr Jonny Hill Ian Nutt (e-mail: iann@wrox.com Marta Rampichini (e-mail: rampichini@mat.unimi.it Hayley Ryder Paul Strickland (e-mail: p.m.strickland@livjm.ac.uk Publications We maintain a list of our publications , which includes PostScript copies of some recent preprints. There are also some braid programs , mainly in Pascal, for calculating a number of knot invariants. Areas of Interest Hugh's interests include: Fibred knots and links.

16. Mahdavi SUNY Potsdam, NY, USA; 26 June 2003. http://www2.potsdam.edu/mahdavk/Conf.htm

Math. Dept. Registration Financial Support SUNY Potsdam ... Map of Parking Lots Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics. SUNY Potsdam June 2-6, 2003 Speakers S CHEDULES ABSTRACTS This workshop investigates the interactions between Representation Theories, Knot Theory, Topology, quantum Field Theory, Category Theory, and Mathematical Physics. This conference will be of great benefit to the researchers, recent Ph.Ds, and graduate students. Some financial support is available for graduate students, recent Ph.Ds, and others who are qualified. REGISTRATION Total cost of room and board, on Campus, is $206.50 Participants who choose to stay on campus will be housed in Draime Hall SUNY Potsdam Map) Off Campus housing Hotel listing (you need to make your own reservation) a block of rooms has been reserved at Clarkson Inn. For reservation please call 1 800 790 6970, before May 15, 2003($89.00 for single, and$99.00 for double, per night). you need to mention SUNY Potsdam math. conference.

17. Liverpool Knot Theory Group: Publication List Liverpool University knot theory Group Articles and Preprints (1987 onwards). J. knot theory Ramif. 1 (1992), 203206. Gzipped PostScript version (42K). http://www.liv.ac.uk/~su14/knotprints.html

Liverpool University Knot Theory Group Articles and Preprints (1987 onwards) Copies of the following papers can be requested by sending e-mail to morton@liv.ac.uk You can download PostScript versions of some of the recent preprints. This list can be found at URL http://www.liv.ac.uk/~su14/knotprints.html or by following links from http://www.liv.ac.uk/maths/ Programs for some knot theory calculations can be found in the list of programs of the Liverpool Knot Theory group You may also enjoy a collection of material on the Borromean Rings H.R.Morton and H.B.Short, `The 2-variable polynomial of cable knots'. Math. Proc. Camb. Philos. Soc. H.R.Morton, `Polynomials from braids'. In `Braids', ed. Joan S. Birman and Anatoly Libgober, Contemporary Mathematics 78, Amer. Math. Soc. (1988), 375-385. H.R.Morton and P.Traczyk, `The Jones polynomial of satellite links around mutants'. In `Braids', ed. Joan S. Birman and Anatoly Libgober, Contemporary Mathematics 78, Amer. Math. Soc. (1988), 587-592. P.R.Cromwell

18. Knot Theory Online - The Web Site For Learning More About Mathematical Knot Theo KT HISTORY History of knot theory. INTRO TO KNOTS What are knots? It is the simplest of all knots. 2) The Central Problem of knot theory ^back to top. http://www.freelearning.com/knots/intro.htm

Intro to Knots This page introduces you to the basics of mathematical Knot Theory, with terms and pictures. Links on this site: [HOME] [HISTORY] [INTRO] [ADVANCED] ... KT HOME Main Page KT HISTORY History of Knot Theory INTRO TO KNOTS What are knots? ADVANCED KT Knot Theory in the Real World KT ACTIVITIES Online activities with knots for you to try KNOT FUNNY Interesting facts, knot-knot jokes, and knotty pictures... INTRODUCTION TO KNOTS: On this page you can view each of the following topics, just click to jump to each section: 1) What is a "mathematical" knot? 2) The Central Problem of Knot Theory 3) How do we work with knots? (The Reidemeister moves) 4) Classifying different knots ... 6) Close cousins - Knots vs. Links 1) What is a "mathematical" knot? [^back to top] In order to get started working with knots, we need to understand what mathematicians mean by the term "knots". A "mathematical" knot is just slightly different from the knots we see and use every day. First, take a piece of string or rope. Tie a knot in it. Now, glue or tape the ends together. You have created a mathematical knot.

19. Links To Low-dimensional Topology Topics General, Conferences, Pages of Links, knot theory, 3manifolds, Journals. http://www.math.unl.edu/~mbritten/ldt/ldt.html

Links to low-dimensional topology Any comments/suggestions? Send them to me! Enter your comments here: Most recent additions: hard to say, I've stopped keeping track... This page was getting just a little too large, so I've cut it into pieces. General Conferences Pages of Links Knot Theory ... Home pages

20. Knots On The Web Knots on the Web Presents a directory of knotrelated Web sites, compiled by Peter Suber. Lists resources on knot tying, knot theory, and knot art. Offers access to information on related software http://rdre1.inktomi.com/click?u=http://www.earlham.edu/~peters/knotlink.htm&

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