Science Fair Project Encyclopedia Knot theory is a branch of
topology that was inspired by observations, as the name
suggests, of knots. But progress in the field no longer depends
on experiments with twine. Knot theory concerns itself with
abstract properties of theoretical knots — the spatial
arrangements that in principle could be assumed by a loop of
string. In mathematical jargon, knots are embeddings of the
closed circle in three-dimensional space. An ordinary knot is
converted to a mathematical knot by splicing its ends together.
The topological theory of knots asks whether two such knots can
be rearranged to match, without opening the splice. The question
of untying an ordinary knot has to do with unwedging tangles of
rope pulled tight. A knot can be untied in the topological
theory of knots if and only if it is equivalent to the unknot, a
circle in 3-space. Knot theory originated in an idea of Lord
Kelvin's (1867), that atoms were knots of swirling vortices in
the æther (also known as 'ether'). He be