High Quality Content by WIKIPEDIA articles! In mathematics, an tangle can mean one of two related concepts: * In John Conway's definition, a 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 2n marked points on the ball's boundary. * In link theory, a tangle is an embedding of n arcs and m circles into mathbf{R}^2 times [0,1] – the difference from the previous definition is that it includes circles as well as arches, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance.

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