**Tangle Theory**

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 Theory: Tangle Diagrams, Rational and Algebraic Tangles, Conway Notation, Applications

### Other articles related to "tangle theory, tangles":

**Tangle Theory**- Applications

...

**Tangles**have been shown to be useful in studying DNA topology ... The action of a given enzyme can be analysed with the help of

**tangle theory**...

### Famous quotes containing the words theory and/or tangle:

“The great tragedy of science—the slaying of a beautiful *theory* by an ugly fact.”

—Thomas Henry Huxley (1825–1895)

“When one has come to accept a certain course as duty he has a pleasant sense of relief and of lifted responsibility, even if the course involves pain and renunciation. It is like obedience to some external authority; any clear way, though it lead to death, is mentally preferable to the *tangle* of uncertainty.”

—Charles Horton Cooley (1864–1929)