Karl Jones: Created page with "In mathematics, a '''knot''' is an embedding of a circle in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies)...."

2016-08-29T15:40:16Z

Created page with "In mathematics, a '''knot''' is an embedding of a circle in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies)...."

New page

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

== Description ==

A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed—there are no ends to tie or untie on a mathematical knot.

Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account.

The term knot is also applied to embeddings of {\displaystyle S^{j}} S^j in {\displaystyle S^{n}} S^{n}, especially in the case {\displaystyle j=n-2} j=n-2.

The branch of [[mathematics]] that studies knots is known as [[knot theory]], and has many simple relations to [[graph theory]].

== See also ==

* [[Knot theory]]
* [[List of mathematical knots and links]]
* [[Rosette (design)]]

== External links ==

* [https://en.wikipedia.org/wiki/Knot_(mathematics) Knot (mathematics)]] @ Wikipedia

[[Category:Mathematics]]

Knot (mathematics) - Revision history

Karl Jones: Created page with "In mathematics, a '''knot''' is an embedding of a circle in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies)...."