How Mathematics
gets into Knots

In order to talk mathematically about knots, we have to show them in some kind of way, to have a method of describing them. We can do this for the simplest knots in a lecture by using a piece of string or rope, which nicely shows the 3-dimensional nature of the object. But even this gets difficult for more complicated knots, since the string becomes difficult to handle and fairly quickly it gets difficult to understand what is going on. So we resort to drawing and pictures.

In mathematics we look at knotted and unknotted loops of string and analyse the forms and relationships between them. So here is the unknot and some common knots.

Unknot

Trefoil

Figure Eight

Cinquefoil

Granny Knot

Stevedore's Knot

Reef Knot

Trefoil	Figure Eight
Cinquefoil	Granny Knot
Stevedore's Knot	Reef Knot

On this exhibition there is a table of knots. In fact, it lists only prime knots up to crossing number 9 and does not distinguish between a knot and its mirror image. But it does give an idea of the complexity of the problem.

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