**Tangle (mathematics)**

In knot theory, a branch of mathematics, a **pretzel link** is a special kind of link. A pretzel link which is also a knot (i.e. a link with one component) is a **pretzel knot**.

In mathematics, a **tangle** can mean one of two related concepts:

- In John Conway's definition, an
*n*-**tangle**is a proper embedding of the disjoint union of*n*arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2*n*marked points on the ball's boundary. - In link theory, a tangle is an embedding of
*n*arcs and*m*circles into – the difference from the previous definition is that it includes circles as well as arcs, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance.

The balance of this article discusses Conway's sense of tangles; for the link theory sense, see that article.

Two *n*-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. **Tangle theory** can be considered analogous to knot theory except instead of closed loops we use strings whose ends are nailed down. See also braid theory.

Read more about Tangle (mathematics): Tangle Diagrams, Rational and Algebraic Tangles, Conway Notation, Applications

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### Famous quotes containing the word tangle:

“To *tangle* Adams race

In’s stratagems”

—Edward Taylor (1645–1729)