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Examples of different knots including the trivial knot (top left) and the trefoil knot (below it) A knot diagram of the trefoil knot, the simplest non-trivial knot. In topology, knot theory is the study of mathematical knots.
3 1 knot/Trefoil knot - (2,3)-torus knot, the two loose ends of a common overhand knot joined together 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 ...
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 example, are always tame.
Stevedore knot (mathematics), a prime knot with crossing number 6; Three-twist knot is the twist knot with three-half twists, also known as the 5 2 knot. Trefoil knot A knot with crossing number 3; Unknot; Knot complement, a compact 3 manifold obtained by removing an open neighborhood of a proper embedding of a tame knot from the 3-sphere ...
For example, if s=2, then 𝜁(s) ... You probably haven’t heard of the math subject Knot Theory. It’s taught in virtually no high schools, and few colleges. The idea is to try and apply ...
In knot theory, prime knots are those ... 6 3 knot: 6 3: 6a1 4 8 10 2 12 6 [2112] ... List of mathematical knots and links; Knot tabulation (−2,3,7) pretzel knot; Notes
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.
This is a list of mathematical theories. Almgren–Pitts min-max theory; Approximation theory; ... Knot theory; L-theory; Lattice theory; Lie theory; M-theory ...