When two knots are the same

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 to ...

The Reidermeister Moves

This illustrates a very important feature of mathematics: we reduce a complicated process to a sequence of simple steps.

Classification

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© Mathematics and Knots, U.C.N.W.,Bangor, 1996 - 2002
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