Difference between revisions of "Knot (mathematics)"
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Latest revision as of 08:40, 29 August 2016
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
External links
- Knot (mathematics)] @ Wikipedia
