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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 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.
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot").
Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3.
A (3,−7)-3D torus knot. EureleA Award showing a (2,3)-torus knot. (2,8) torus link. In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R 3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p ...
Skein relations are a mathematical tool used to study knots. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One way to answer the question is using knot polynomials, which are invariants of the knot. If two diagrams have different polynomials, they represent
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. [1] [2] Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable / with integer coefficients. [3]
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]