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The notion of a knot has further generalisations in mathematics, see: Knot (mathematics), isotopy classification of embeddings. Every knot in the n -sphere S n {\displaystyle \mathbb {S} ^{n}} is the link of a real-algebraic set with isolated singularity in R n + 1 {\displaystyle \mathbb {R} ^{n+1}} ( Akbulut & King 1981 ).
A polygonal knot is a knot whose image in R 3 is the union of a finite set of line segments. [6] A tame knot is any knot equivalent to a polygonal knot. [6] [Note 2] Knots which are not tame are called wild, [7] and can have pathological behavior. [7] In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for ...
Figure-eight knot (mathematics) the only 4-crossing knot; Granny knot (mathematics) and Square knot (mathematics) are a connected sum of two Trefoil knots; Perko pair, two entries in a knot table that were later shown to be identical. Stevedore knot (mathematics), a prime knot with crossing number 6; Three-twist knot is the twist knot with ...
4 1 knot/Figure-eight knot (mathematics) - a prime knot with a crossing number four; 5 1 knot/Cinquefoil knot, (5,2)-torus knot, Solomon's seal knot, pentafoil knot - a prime knot with crossing number five which can be arranged as a {5/2} star polygon ; 5 2 knot/Three-twist knot - the twist knot with three-half twists
A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory . Implicit in this definition is that there is a trivial reference link, usually called the unlink , but the word is also sometimes used in context where there is no notion of a trivial link.
The Game of Trees is a Mad Math Theory That Is Impossible to Prove ... The Amazing Math Inside the Rubik’s Cube. Knot theorists’ holy grail problem was an algorithm to identify if some tangled ...
Figure-eight knot of practical knot-tying, with ends joined. In knot theory, a figure-eight knot (also called Listing's knot [1]) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot.
The first work of knot theory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait. [3] In recreational mathematics, the Borromean rings were popularized by Martin Gardner, who featured Seifert surfaces for the Borromean rings in his September 1961 "Mathematical Games" column in Scientific American. [19]