In drawing pictures of knots, we represent lace and interlace by crossings. The more crossings there are the more complicated is the picture.

Here is a picture of a trefoil with nine crossings. By twisting
and crumpling, you can make a picture of a knot with as many crossings
as you can draw! So to find out about any knot, it is natural
to look for a picture of it with the smallest number of crossings.
The number of crossings in that picture is called the
**crossing number** of the knot.

The unknot has crossing number 0. Any picture with only 1 or We have not drawn all the knot pictures with 2 crossings, and
leave you to draw all those with 2 or with 3 crossings.

**2 crossings** must be the unknot. Can you see why?

The trefoil has crossing number 3. On another page, we give a
diagram of a trefoil with The figure eight has crossing number 4. Classifying knots according
to crossing numbers is one method of trying to understand the
infinite complications of knots and tangles.

**4 crossings**.

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

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