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Prime knot

Index Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. [1]

15 relations: Chirality (mathematics), Connected sum, Coprime integers, Crossing number (knot theory), Figure-eight knot (mathematics), Horst Schubert, Integer, Knot (mathematics), Knot theory, List of prime knots, Mirror image, Torus, Torus knot, Trefoil knot, Unknot.

Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.

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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

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Figure-eight knot (mathematics)

In knot theory, a figure-eight knot (also called Listing's knot or a Cavendish knot) is the unique knot with a crossing number of four.

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Horst Schubert

Horst Schubert (11 June 1919 – 2001) was a German mathematician.

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An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Knot (mathematics)

In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

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Knot theory

In topology, knot theory is the study of mathematical knots.

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List of prime knots

In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum.

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Mirror image

A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface.

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In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Torus knot

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.

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Trefoil knot

In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.

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The unknot arises in the mathematical theory of knots.

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Redirects here:

Composite knot, Composite link, Prime knots, Prime link.


[1] https://en.wikipedia.org/wiki/Prime_knot

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