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Topic: Knot mathematical

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	Knot (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space, R
		The simplest nontrivial knots are the trefoil knot and the figure-eight knot.
		In knot theory and 3-manifold theory, oftentimes the adjective "tame" is omitted.
	en.wikipedia.org /wiki/Knot_(mathematical) (273 words)

	Knot theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-11)
		Knot theory is a branch of (The configuration of a communication network) topology that was inspired by observations, as the name suggests, of (Any of various fastenings formed by looping and tying a rope (or cord) upon itself or to another rope or to another object) knots.
		Knot theory concerns itself with abstract properties of (additional info and facts about theoretical knots) theoretical knots — the spatial arrangements that in principle could be assumed by a loop of string.
		Knot theory originated in an idea of (additional info and facts about Lord Kelvin) Lord Kelvin's (1867), that atoms were knots of swirling vortices in the (additional info and facts about æther) æther (also known as 'ether').
	www.absoluteastronomy.com /encyclopedia/k/kn/knot_theory.htm (987 words)

	Mathematical knots (Site not responding. Last check: 2007-10-11)
		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.
		Thus a mathematical knot is somewhat different from the usual idea of a knot, that is, a piece of string with free ends.
		Knots that are equivalent to the unit circle are considered to be unknotted or trivial.
	www.cs.ubc.ca /nest/imager/contributions/scharein/knot-theory/knot-theory.html (928 words)

	Svetlana Varchenko's Home Page
		A knot is a mathematical object, just like number is, and mathematicians ask many of the same questions about knots as they have asked about numbers.
		Two knots are considered to be the same if, when they are made out of rope or some other material you can twist one of them around (without cutting) so that each looks exactly like the other one with all the over- and under-crossings in the same place.
		Some of the ways that knots are classified is by the arrangement of their crossings, the characteristics of their mirror images, and the braids from which they are formed.
	www.unc.edu /~svetlana/knot.htm (669 words)

	Geometry.Net - Math Discover Books: Knot
		Knot Theory by Vassily Manturov (CRC Press) The aim of the present monograph is to describe the main concepts of modern knot theory together with full proofs that would be both accessible to beginners and useful for professionals.
		Knot theory has been a branch of mathematics that has been around for over a century, and now is finding applications in mnay areas, some of these being electrical circuit analysis, genetics, dynamical systems, and cryptography.
		Knot theory now is an established branch of mathematics, and it involves the use of tools from topology, analysis, and algebra.
	www.geometry.net /math_discover_bk/knot.html (5400 words)

	Ivars Peterson's MathTrek - The Tangled Task of Distinguishing Knots
		In this context, a knot is a one-dimensional curve that winds through itself in three-dimensional space, finally catching its tail to form a closed loop.
		One approach to labeling knots is to use the arrangement of the crossings in a knot diagram to produce an algebraic expression for that knot.
		To solve the problem of distinguishing among knots, mathematicians have tried to find schemes for labeling them in such a way that two knots having the same label are really equivalent—even when their diagrams may appear different—and that two knots with different labels are truly different.
	www.maa.org /mathland/mathtrek_02_24_03.html (1038 words)

	DNA AND KNOT THEORY
		Mathematical knots are represented by two-dimensional diagrams that can be thought of as the shadow cast by a three-dimensional knot.
		The only way to untie a mathematical knot is to cut through the knot so that the strand that was lying on top is now underneath.
		Mathematical knots may have values for writhe and crossing number that are much higher than the ideal number if they have been moved smoothly through space to a more complicated form.
	www.tiem.utk.edu /~gross/bioed/webmodules/DNAknot.html (1424 words)

	Read This: Why Knot? An Introduction to the Mathematical Theory of Knots
		Knot theory is a hands-on subject which shouldn't just be read about: one would miss too much of the fun.
		After the trefoil knot is introduced, it is carefully noted that no amount of fiddling with the knot and not being able to untie it can show that it is not equivalent to the unknot.
		An Introduction to the Mathematical Theory of Knots, by Colin Adams.
	www.maa.org /reviews/whyknot.html (868 words)

	Knots and physics
		He was interested in knots because of electromagnetic considerations and in a letter to Tait written on the 4 December 1867 he rediscovered an integral formula counting the linking number of two closed curves which Gauss had discovered, but had not published, in 1833.
		Although his approach contained no mathematical rigour, still it is interesting to note that at this early stage Maxwell had defined the "Reidemeister moves" which would be shown to be the fundamental moves in modifying knots in the 1920s.
		In fact it is not, but for alternating knots, it is an invariant and this fact is a consequence of Tait's second conjecture (a theorem since 1993).
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Knots_and_physics.html (2827 words)

	Ideas, Concepts and Definitions (Site not responding. Last check: 2007-10-11)
		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.
	www.c3.lanl.gov /mega-math/gloss/knots/knots.html (65 words)

	The KnotPlot Site (Site not responding. Last check: 2007-10-11)
		Knots can be loaded from a database of almost 1000 knots and links or sketched by hand in three dimensions.
		Also, knots may be constructed via the Conway notation or using a tangle calculator.
		Pacific Institute for the Mathematical Sciences, and the Centre for Experimental and Constructive Mathematics.
	www.cs.ubc.ca /nest/imager/contributions/scharein/KnotPlot.html (396 words)

	Poster Project, Knots Poster (Site not responding. Last check: 2007-10-11)
		Knot theory is the rigorous mathematics which can distinguish between different knots.
		Mathematical knots are an imagined model of the physical knot-making process.
		Knot Theory has a very pretty presentation and quite a bit of mathematics.
	www.math.sunysb.edu /posterproject/www/materials/knots/knots.html (440 words)

	Chinese Knotting Glossary of Terms (Site not responding. Last check: 2007-10-11)
		a loop of string on the knot that is not a structural part of the knot.
		while there is probably a formal mathematical knot theory use for the term, I use it to describe a logical progression of knots that I have tied in a single column of knots, usually used to illustrate the main knot image on a page.
		When tying knots in sequence or aggregate there will usually be at least 2 loose end ears on a knot where the path of the cords enter and leave the knot.
	www.chineseknotting.org /glossary.html (392 words)

	Overhand knot (Site not responding. Last check: 2007-10-11)
		The overhand knot is not strong, so it is not used in situations where you might expect great force.
		The overhand knot is commonly tied in a bight formed at the end of a rope, forming the Overhand Loop.
		Thumb Knot (Overhand Knot) This is the simplist knot of all.
	www.knotwork.ca /?Category=Overhand%20knot (481 words)

	Knots on the Web (Peter Suber)
		Maintained by Jan Korpegård. Under each knot, Korpegård gives the knot's name in 10 languages, and asks readers of other languages to send him the names of the same knots in their languages; he even provides the form for submitting the names electronically.
		A Bibliography of Literature on Knots and Braids.
		Decorative knotting, some for sale, by a man who calls himself the world's best (which may or may be true), and who thinks of himself as alone in his art (which is fortunately false).
	www.earlham.edu /~peters/knotlink.htm (6783 words)

	Untying the Gordian Knot
		Thus, the Gordian knot was most likely constructed by first splicing the two ends of a length of rope to form a loop, and then "tying" the loop up (i.e.
		Under those assumptions, if the Gordian knot were really an unkotted loop, then it would have been possible to untie it, i.e., to manipulate it so it was in the form of a simple loop that does not cross itself.
		Physicists are interested in knots because the latest theories of matter postulate that everything is made up of tightly coiled (and maybe knotted) loops of space-time, and biologists are interested in knots because the long, string-like molecules of DNA coil themselves up tightly to fit inside the cell.
	www.maa.org /devlin/devlin_9_01.html (939 words)

	Knot Theory Online - The Web Site for Learning More about Mathematical Knot Theory
		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.
		Advanced Knot Theory Topics - Once you understand the concepts in the introduction to knots, this page expands your knowledge with connected sums, composite and prime knots, stick knots, wild knots, and even has a section on coloring knots and links and why coloring is such an important topic to mathematicians.
		We are especially interested in hearing from teachers who have used knots in the classroom and students who have been motivated to study knots either in the classroom or on their own.
	www.freelearning.com /knots (563 words)

	Open Directory - Science: Math: Topology: Knot Theory (Site not responding. Last check: 2007-10-11)
		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 Theory of Knots.
		Mathematics and Knots Exhibition - High school level introduction to knot theory.
	dmoz.org /Science/Math/Topology/Knot_Theory (751 words)

	AT&T Worldnet Service - Directory
		Nearly all of the images here were created with KnotPlot, a program to visualize and manipulate mathematical knots in three and four dimensions.
		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.
		Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format).
	www.att.net /cgi-bin/webdrill?catkey=gwd/Top/Science/Math/Topology/Knot_Theory (707 words)

	'Why Knot?' comic book teaches mathematical theory
		Every page is filled with humorous and instructional illustrations, turning the challenging study of knot theory and the application of knot theory to DNA into an accessible adventure.
		Its award-winning author received the Mathematical Association of America Distinguished Teaching Award in 1998 and the Robert Foster Cherry Great Teaching Award in 2003, which recognized the outstanding teacher in North America in any discipline.
		He is also the author of a more detailed introduction to knot theory, "The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots" (1994).
	www.eurekalert.org /pub_releases/2004-07/wc-kc070804.php (447 words)

	Knot Theory Online - The Web Site for Learning More about Mathematical Knot Theory
		If you have a knot site you'd like to add, please feel free to email mrpayne@freelearning.com with your site name, and please feel free to link to our site and activities.
		Knot Theory page for tons of information on the subject.
		Knots on the Web* - The most complete and exhaustive collection of links to every site you can imagine on knot tying, knot theory, knot art, knot software, knot books, and even a knot** gallery for reference and enjoyment.
	www.freelearning.com /knots/fun.htm (1122 words)

	Joseph Malkevitch's Knots Bibliography
		Kawauchi, A., A Survey of Knot Theory, Birkhauser, Boston, 1996.
		Lickorish, W., An Introduction to Knot Theory, Springer-Verlag, New York, 1997.
		Livingston, C., Knot Theory, Mathematical Association of America, Washington, 1993.
	www.york.cuny.edu /~malk/biblio/knots-biblio.html (205 words)

	Dror Bar-Natan: Talks: Queens-040123 (Site not responding. Last check: 2007-10-11)
		Over the last 20 years, knot theorists have been extremely good at borrowing ideas from other fields.
		We've borrowed from Mathematical Physics and borrowed from Algebra and we have a Beautiful Theory of Knot Invariants that can claim deep heritage on either side.
		The Mathematical Physics and Algebra underlying the Jones polynomial are deep and substantial, and there are all reasons to believe that a successful resolution of Khovanov's challenge will be the same.
	www.math.toronto.edu /~drorbn/Talks/Queens-040123/Queens-040123.html (211 words)

	The KnotPlot Site (Site not responding. Last check: 2007-10-11)
		Interactive knot viewer (randomly chosen knot, requires Java): smooth knots minimal-stick knots equilateral minimal-stick knots crazy knots.
		Lissajous knots) may be created on the fly.
		KnotPlot is an OpenGL program that runs on most types of computers.
	www.pims.math.ca /knotplot (396 words)

	Poster Project, The Definition of a Knot (Site not responding. Last check: 2007-10-11)
		a mathematical knot is an object which can be made by embedding a circle in three-dimensional space without tearing.
		We want mathematical knots to be topologically the same as circles.
		a mathematical knot is an object in three-dimensional space which is homeomorphic to a circle.
	www.math.sunysb.edu /posterproject/www/materials/knots/definition.html (186 words)

	Math Trek: The Tangled Task of Distinguishing Knots, Science News Online, Feb. 22, 2003 (Site not responding. Last check: 2007-10-11)
		Over the years, mathematicians have developed a variety of knot invariants, often expressed in the form of a polynomial algebraic expression.
		He is the author of The Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect, The Jungles of Randomness, and Fragments of Infinity.
		He is coauthor of the children's books Math Trek: Adventures in the MathZone and Math Trek 2: A Mathematical Space Odyssey.
	www.sciencenews.org /articles/20030222/mathtrek.asp (1143 words)

	No Title
		Coach of the International Mathematical Olympiad Team of India, Homi Bhabha Center of Science Education, Mumbai, India, 2004, 2005.
		The noncommutative A-ideal of a (2p+1,2)-torus knot determines its Jones polynomial
		Coordinator of the grading, 40th International Mathematical Olympiad, Bucharest, Romania, 1999, and of the 42nd International Mathematical Olympiad, Washington, USA, 2001.
	www.math.ttu.edu /~rgelca/cv.html (1300 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		The knot book: an elementary introduction to the mathematical theory of knots
		Knotted doughnuts and other mathematical entertainments See pp.
		The mathematical tourist: snapshots of modern mathematics See pp.
	www.smithlib.org /page_young_adult_math_fair_k.html (60 words)

	The Knot Room
		Featured exclusively at the Knot Room are animations made with Lloyd Burchills' brilliant application Knot.
		I will be considering submissions from time to time, so if you are a devotee of Knot, and wish to show your work in this venue, please peruse the Submission Guidelines.
		The display will be growing periodically, showcasing the possibilities of Knot.
	www.redlipstick.net /knotroom (235 words)

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