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# Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. [1]

## Almost all

In mathematics, the term "almost all" means "all but a negligible amount".

## Ambient isotopy

In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold.

## Chiral knot

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image.

## Conway notation (knot theory)

In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear.

## 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.

## 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.

## Hale Trotter

Hale Freeman Trotter (born 30 May 1931, Kingston, Ontario) is a Canadian-American mathematician, known for the Hale product formula, the Steinhaus–Johnson–Trotter algorithm, and the Lang-Trotter conjecture.

## Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## 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 mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.

## Mathematics

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

## On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

In the mathematical theory of knots, a pretzel link is a special kind of link.

## Ralph Fox

Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician.

## Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

## Trefoil knot

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

## Tunnel number

In mathematics, the tunnel number of a knot, as first defined by Bradd Clark, is a knot invariant, given by the minimal number of arcs (called tunnels) that must be added to the knot so that the complement becomes a handlebody.

## References

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