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 World Catalog > Science > Math > Topology > Knot Theory

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World Catalog > Science > Math > Topology > Knot Theory

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.

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

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.

http://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.html

Geometry and the Imagination

Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.

http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html

Graand

Free Classified Ads Portal

www.graand.com

The Geometry Junkyard: Knot Theory

A page of links on geometric questions arising from knot embeddings.

http://www.ics.uci.edu/~eppstein/junkyard/knot.html

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.

http://www.maths.ed.ac.uk/~aar/knots/index.htm

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.

http://www.pims.math.ca/knotplot/

Knot Theory

Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations.

http://www.mapleapps.com/categories/mathematics/Knot%20theory/html/Knots.htm

Knot Theory

An overview of knot theory from Mathworld

http://mathworld.wolfram.com/topics/KnotTheory.html

Knot Theory Group University of Liverpool

Links to preprints and to programs written in pascal for doing knot calculations.

http://www.liv.ac.uk/~su14/knotgroup.html

The Knot Theory Home Page

Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations.

http://library.thinkquest.org/12295/

Knot Theory Invariants: The HOMFLY Polynomial

A brief article on the HOMFLY polynomial and how it is calculated.

http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html

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.

http://www.inst.bnl.gov/~wei/contents.html

Knotscape

By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.

http://www.math.utk.edu/~morwen/knotscape.html

Mathematics and Knots Exhibition

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/

Megamath Knot Theory Page

An introductory overview of knot theory.

http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html

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.

http://www.math.utk.edu/~morwen/

New Knot Tables

Covers families of knots of p, pq, p1q, p11q, p111q, pqr, pq1r types. Explains properties and notations. Includes diagram photos.

http://members.tripod.com/vismath7/knotab/

Pictures of Knots

A table of graphics of all knots of up to nine crossings. Also includes pictures of some links.

http://www.math.unl.edu/~mbrittenham2/ldt/table9.gif

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.

http://website.lineone.net/~m.p/sf/menu.html

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.

http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html

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''.

http://www.tcm.phy.cam.ac.uk/~tmf20/

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. [PDF]

http://www.ams.org/notices/199505/sumners.pdf

Tax rich at higher rate, says TUC

People earning more than £100,000 a year should pay higher tax rates, the Trades Union Congress says.

news.bbc.co.uk

Your pictures

Storms rage in north-east and central England

news.bbc.co.uk

Angola's troubled election closes

Voting in Angola's first parliamentary elections in 16 years closes after second day.

news.bbc.co.uk

The Wrestler scoops Golden Lion

The Wrestler, starring Mickey Rourke, wins the coveted Golden Lion for best picture at the Venice film festival.

news.bbc.co.uk

Bhutto's widower wins presidency

Asif Ali Zardari, the widower of former Prime Minister Benazir Bhutto, wins a sweeping victory in Pakistan's presidential election.

news.bbc.co.uk

Wrestle mania

Mickey Rourke wows Venice with latest movie

news.bbc.co.uk

In pictures

Paralympic Games opens in Beijing

news.bbc.co.uk

Polish pair comes first in Euro dance contest

Poland won the second Eurovision Dance Contest, which was held in Glasgow before a television audience of millions.

news.bbc.co.uk

Scots fans turned away from game

Hundreds of football fans are refused entry to the stadium for Scotland's World Cup qualifier against Macedonia.

news.bbc.co.uk

Good day Darling?

How will the TUC welcome the chancellor?

news.bbc.co.uk

Heat on Brown over cost of energy

The prime minister is accused of letting households "plunge into fuel poverty" by not acting to address rising energy prices.

news.bbc.co.uk

Week in pictures

Striking images from around the world this week

news.bbc.co.uk

Mother's shock over mansion deaths

The mother of a man thought to have killed his family and torched his mansion before killing himself tells of her shock.

news.bbc.co.uk

What do you want to talk about?

What do you want the world to talk about?

news.bbc.co.uk

Teenager dies in flooding crash

A 17-year-old dies when a vehicle overturns in a flooded river after one of the wettest 48 hours on record.

news.bbc.co.uk

New hurricane menaces Caribbean

The Caribbean braces for Hurricane Ike, just days after Tropical Storm Hanna left 500 dead in Haiti.

news.bbc.co.uk

Murray leading when rain arrives

Britain's Andy Murray leads world number one Rafael Nadal by two sets to love when rain suspends their US Open semi-final.

news.bbc.co.uk

Khan knocked out inside first minute

Amir Khan is knocked out inside the first minute of his WBO intercontinental lightweight title defence by Breidis Prescott.

news.bbc.co.uk

Man questioned over baby's murder

A 24-year-old man is arrested and is being questioned about the murder of a 14-week-old baby boy.

news.bbc.co.uk

Deadly rockslide hits Cairo homes

At least 24 people have died after a rockslide destroys homes in a shanty town in the Egyptian capital, emergency services say.

news.bbc.co.uk

Flood fears as river levels rise

Flooding may continue to affect parts of England and Wales for several days, the Environment Agency warns.

news.bbc.co.uk

Cole double rescues nervy England

England labour to a 2-0 World Cup qualifying win over Andorra thanks to Joe Cole's second-half brace.

news.bbc.co.uk

Data on 5,000 justice staff lost

A computer disc containing details of thousands of prison officers and other justice system employees has gone missing.

news.bbc.co.uk

Lottery results: Are you a winner?

Check the numbers from Saturday's Lotto draw.

news.bbc.co.uk

Climate change

Green Party's first leader takes aim at Westminster

news.bbc.co.uk