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Knot -- from Wolfram MathWorld
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Last updated: Mon Dec 1 2008
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Topology > Knot
Theory > Knots >
Interactive Entries > Interactive Demonstrations >
Knot
In mathematics, a knot is defined as a closed , non-self- intersecting curve that is embedded in three dimensions and
cannot be untangled to produce a simple loop (i.e., the unknot ).
While in common usage, knots can be tied in string and rope such that one or more
strands are left open on either side of the knot, the mathematical theory of knots
terms an object of this type a " braid "
rather than a knot. To a mathematician, an object is a knot only if its free ends
are attached in some way so that the resulting structure consists of a single looped
strand.
A knot can be generalized to a link , which
is simply a knotted collection of one or more closed strands.
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