Knot Theory

Bronze broach from the Iron Age, found on Gottland, Sweden

Relevant examples from Escher's work:

• Knots
• Knot(second version)

Introduction

Knots have been used in decorations for centuries. Knotted figures appear in Celtic and Nordic art as well as for instance in the famous Book of Kells and the Lindisfarne Gospels. We think of a knot as a string that is knotted up, and then has the ends tied together to prevent it from becoming undone. Mathematically we would say that a knot is an embedding of the circle in 3-space.

The knot as an unending loop which is twisted up is sometimes seen as a symbol of the infinite. In Ireland the Celtic crosses are often shown as intricate knotted figures and

Knot Tables

In the 19th century Tait, Kirkman and Little started tabulating the knots in so called knot tables. The knots are listed in order grouped by the number of crossings. Below you see a copy of the knot table for knots with 3 to 7 crossings. As you see there is exactly one knot with 3 crossongs. This knot is often called the trefoil knot. There is also a unique knot with four crossings: the figure-eight-knot. In some pictures part of the knot will resemble a figure eight.

The original image can be found at The knot Atlas page.. On this site you can click on the knots to obtain more information.

References

Knot Theory page, Wikipedia