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A (3,−7)-3D torus knot.
EureleA Award showing a (2,3)-torus knot.
(2,8) torus link

{{#invoke:Hatnote|hatnote}} In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. 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 and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot.

the (2,−3)-torus knot, also known as the left-handed trefoil knot

Torus knot sections
Intro   Geometrical representation   Properties   Connection to complex hypersurfaces   List  See also   References   External links  

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A (3,−7)-3D torus knot.
EureleA Award showing a (2,3)-torus knot.
(2,8) torus link

{{#invoke:Hatnote|hatnote}} In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. 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 and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot.

the (2,−3)-torus knot, also known as the left-handed trefoil knot

Torus knot sections
Intro   Geometrical representation   Properties   Connection to complex hypersurfaces   List  See also   References   External links  

PREVIOUS: IntroNEXT: Geometrical representation
<<>>