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In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. For each crossing one comes across while traveling in this direction, if the strand un
In an attempt to make a periodic table of the elements, P. G. Tait, C. N. Little and others started to attempt to count all possible knots. [3] Because their work predated the invention of the digital computer, all work had to be done by hand.
KnotInfo: Table of Knot Invariants and Knot Theory Resources; The Knot Atlas — detailed info on individual knots in knot tables; KnotPlot — software to investigate geometric properties of knots; Knotscape — software to create images of knots; Knoutilus — online database and image generator of knots
The unknotting number of a knot is always less than half of its crossing number. [2] This invariant was first defined by Hilmar Wendt in 1936. [3] Any composite knot has unknotting number at least two, and therefore every knot with unknotting number one is a prime knot. The following table show the unknotting numbers for the first few knots:
The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan, who maintains the current site with Scott Morrison. According to Schiller, the site contains, "beautiful illustrations and detailed information about knots," as does KnotPlot.com. [1]
7 4 knot, "endless knot" 8 18 knot, "carrick mat" 10 161 /10 162, known as the Perko pair; this was a single knot listed twice in Dale Rolfsen's knot table; the duplication was discovered by Kenneth Perko; 12n242/(−2,3,7) pretzel knot (p, q)-torus knot - a special kind of knot that lies on the surface of an unknotted torus in R 3
Please help by editing the article to make improvements to the overall structure. ( April 2024 ) ( Learn how and when to remove this message ) The (−2,3,7) pretzel knot has two right-handed twists in its first tangle , three left-handed twists in its second, and seven left-handed twists in its third.
In knot theory, a knot move or operation is a change or changes which preserve crossing number. [1] Operations are used to investigate whether knots are equivalent, prime or reduced . Knot moves or operations include the flype , Habiro move , Markov moves (I. conjugation and II. stabilization), pass move , Perko move , and Reidemeister moves (I ...