A knotted loop of string has essentially the same kind of `knottiness',
however it is pulled, twisted or crumpled. This means that all
the above diagrams really show the same knot. The final picture is just the unknot in disguise!
Any knot can be pictured in any number of forms. The key point
of a picture is the way the crossings are arranged. If two pictures
represent the same knot, then one picture can be changed into
the other by repeated use of simple moves. You may deform the picture without changing any crossing as in ...
or you can remove, insert or change some of the crossings according
This illustrates a very important feature of mathematics: we reduce
a complicated process to a sequence of simple steps.
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© Mathematics and Knots, U.C.N.W.,Bangor, 1996 - 2002
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