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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. [1]

## Alternating knot

In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link.

## Average crossing number

In the mathematical subject of knot theory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of the knot obtained by projection onto the plane orthogonal to the direction.

## Bridge number

In the mathematical field of knot theory, the bridge number is an invariant of a knot defined as the minimal number of bridges required in all the possible bridge representations of a knot.

## DNA

Deoxyribonucleic acid (DNA) is a thread-like chain of nucleotides carrying the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses.

## 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.

## Gel electrophoresis

Gel electrophoresis is a method for separation and analysis of macromolecules (DNA, RNA and proteins) and their fragments, based on their size and charge.

## 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).

## Knot invariant

In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.

## Knot theory

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

In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space.

## Marc Lackenby

Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Normal surface

In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron so that each component of intersection is a triangle or a quad (see figure).

## Peter Tait (physicist)

Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.

## Prime knot

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

## Satellite knot

In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement.

## Stick number

In the mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot.

## 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.

## Trefoil knot

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

## Twist knot

In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together.

## Unknot

The unknot arises in the mathematical theory of knots.

## Unknotting number

In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it.

## 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

## References

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