| Knot_Theory_Group_University_of_Liverpool Links to preprints and to programs written in pascal for doing knot calculations. |
| The_Knot_Theory_Home_Page Elementary introduction to knot theory. Covers the existence of knots, Reidemeister moves and colorations. |
| 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 T |
| 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. |
| 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. |
| 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 cr |
| 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. |
| 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. |
| 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 o |
| 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). |
| ACFnewsource_org\'s_Environment_Coverage Feature stories from U.S. nonprofit organization specializing in research, development and production of news stories on substantive issues, including the environment, for commercial radio and televis |
| Africa2020_-_Environment_and_Sustainable_Development Provides daily environmental stories and information from around the African Union. Also features links to radio broadcasts. |
| Afrol_News_-_Environment News and analysis focused on Africa. In English and Spanish. |
| allAfrica_com__Environment_and_Sustainable_Development Articles, news and reports on issues in Africa. Bilingual English and French. |
| Animal_News_-_theBigZoo_com A variety of animal-related articles from around the web. Includes zoo births & deaths, endangered species updates and scientific discoveries. |
| BNA\'s_EHS_Professional_Information_Center Provides news, analysis, and source materials prepared by the Environment, Health & Safety Division at BNA, Inc. |
| The_Cartoonist_Group Recent cartoons on environmental issues and related topics. |
| E_The_Environmental_Magazine Independent, non-partisian reporting covering personal, community and global isses. Published by Earth Action Network. |
| Earth_Vision Electronic news source covering environmental resources, information, and organizations. |
| EarthWire Daily service managed by UNEP/GRID-Arendal, with headlines compiled from local news sources around the world. |
| Eco_Connections Online magazine features current articles of news and events on the environment and conservation efforts with an emphasis on the Carolinas. Produced by Catawba College. |
| Eco_Media Australian service compiling online news and media releases on environment and conservation. Sources include mainstream news services, environmental organizations, government bodies and political part |
| EDIE_-_Environmental_Data_Interactive_Exchange News on environmental science and issues, with global scope and UK focus. Also includes product announcements, job listings, events announcements, and registered-user access to tenders and RFPs. |
| ENDS_Environment_Daily Fee-based news service covering European environmental policy, regulation and other topics for professionals. |
| The_ENDS_Report UK publication on environmental policy and business for professionals, including environmental analysis, legislation, regulations, and jobs. Requires subscription to view articles. |
| Environment_News_Service News on issues affecting the earth. |
| Environmental_Protection_Magazine On-line publication for environmental professionals. Focus is on environmental compliance. |
| Florida_Environment_Radio Daily feature on issues in and news about Florida's environment. Produced for Florida's public radio stations and The Southwest Florida Council for Environment Education (SWFCEE). |
| Garden_State_EnviroNet Since 1993, NJ's source for environmental news and information. Features: Daily EnviroNews, web site with Calendar, Library, Links, Newsletters, and news from the NJDEP, USEPA, Audubon, Sierra and ma |
| Great_Lakes_Radio_Consortium Provides about 7 environmental stories a week for radio broadcast and makes them available in Real Audio format on this site. |
| Green_Clippings Features articles covering climate change, energy, biodiversity, and sustainable development. Offers newsletter, subscription information, and archive of articles. |
| Green_Dossier Weekly environmental news from Ukraine in English. Also has daily environmental news from all over the world in Russian and Ukrainian. |
| green-techZone News coverage of electronics, energy, and the environment, plus resources, events, and product reviews. |
| Grist_Magazine Provides environmental news topics with humor. Updated every weekday. A project of Earth Day Network. |
AreBorromean links so rare?S. Javan relates the history of the links and describesvarious generalizations with more than three rings.For more history and symbolism of the Borromean rings,see Peter Cromwell'sweb site.Borromeanpaper clips.ABrunnian link. Cutting any one of five links allows the remainingfour to be disconnected from each other, so this is in some sense ageneralization of the Borromean rings. However since each pair of linkscrosses four times, it can't be drawn with circles.Colinear points on knots.Greg Kuperbergshows that a non-trivial knot or link in R3necessarily has four colinear points.
Curvature of knots.Steve Fenner shows that any smooth, simple, closed curve in 3-space must havetotal curvature at least 4 pi.Cut-the-knot logo.With a proof of the origami-folklore that this folded-flat overhandknot forms a regular pentagon.
Detecting the unknot in polynomial time,C. Delman and K. Wolcott, Eastern Illinois U.Figure eight knot / horoball diagram.Research of A. Edmonds into the symmetries of knots,relating them to something that lookslike a packing of spheres.The MSRI Computing Group uses another horoballdiagram as their logo.GeometricArts. Knots, fractals, tesselations, and op art.Formerly QuincyKim's World of Geometry.Geometry and the Imagination in Minneapolis.Notes from a workshop led by Conway, Doyle, Gilman, and Thurston.Includes several sections on polyhedra, knots, and symmetry groups.Hyperbolic Knot.From Eric Weisstein's treasure trove of mathematics.Aaron Kellner Linear Sculpture.Art in the form of geometric tangles of metal and wood rods.Knot art. Keith and Fran Griffin.Knot pictures. Energy-minimized smooth and polygonal knots, from the mingknot evolver, Y. Wu, U. Iowa.KnotPlot.Pictures of knots and links, from Robert Scharein at UBC.Knots on the Web,P. Suber. Includes sections on knot tying and knot art as well as knottheory.Mathematical imagery by Jos Leys.Knots, Escher tilings, spirals, fractals, circle inversions, hyperbolictilings, Penrose tilings, and more.Louis Bel's povray galleries:lespolyhèdres réguliers,knots,andmore knots.Maille Weaves.Different repetitive patterns formed by linked circles along a plane in space,as used for making chain mail. Along with some linear patterns forjewelry chains.Mathematicsin John Robinson's symbolic sculptures. Borromean rings, torusknots, fiber bundles, and unorientable geometries.Meru Foundation appears to beanother sacred geometry site, with animated gifs of torus knotsand other geometric visualizations and articles.Modularity in art.Slavik Jablan explores connections between art, tiling, knotwork, andother mathematical topics.Mutations and knots.Connections between knot theory and dissection of hyperbolic polyhedra.Orthogonal discrete knots.Hew Wolff asks questions about the minimum total length, or the minimum volume of a rectangular box, needed to form different knots as three-dimensional polygons using only integer-length axis-parallel edges.Penrosemandala and five-way Borromean rings.ThePretzel Page. Eric Sedgwick uses animated movies of twisting pretzel knotsto visualize a theorem about Heegard splittings(ways of dividing a complex topological space into two simple pieces).Programming for 3dmodeling, T. Longtin. Tensegrity structures, twisted torus space frames,Moebius band gear assemblies, jigsaw puzzle polyhedra, Hilbert fractal helices,herds of turtles, and more.In search of the ideal knot.Piotr Pieranski applies an iterative shrinking heuristic to find theminimum length unit-diameter rope that can be used to tie a given knot.SnapPea, powerful software for computing geometric properties ofknot complements and other 3-manifolds.Soap films on knots. Ken Brakke, Susquehanna.Space Cubesplastic geometric modeling puzzle basedon a rectangular Borromean link.Square Knots. This article by Brian Hayes for American Scientistexamines how likely it is that a randomlattice polygon is knotted.String figuremathematics, or trivial knot theory.Morwen Thistlethwait,sphere packing, computational topology, symmetric knots,and giant ray-traced floating letters.Trefoilknot stairs. Java animation of an Escher-like infinite stair construction,intended as a Montreal metro station sculpture,by Guillaume LaBelle.Triangulating 3-dimensional polygons.This is always possible (with exponentially many Steiner points)if the polygon is unknotted, but NP-complete if no Steiner points are allowed.The proof uses gadgets in which quadrilaterals arestacked like Pringles to form wires.
UMass Ganglibrary of knots, surfaces, surface deformation movies, and minimal surface meshing software.From the Geometry Junkyard,computationaland recreational geometry pointers.Send email if youknow of an appropriate page not listed here.David Eppstein,Theory Group,ICS,UC Irvine.Semi-automaticallyfilteredfrom a common source file.