# Difference between revisions of "Knot Theory"

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− | [[Image:Knot-Norse-broach.png|right|thumb| | + | [[Image:Knot-Norse-broach.png|right|thumb|200 px|Bronze broach from the Iron Age, found on Gottland, Sweden]] |

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+ | Relevant examples from Escher's work: | ||

* [[Knots]] | * [[Knots]] | ||

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==Introduction== | ==Introduction== | ||

− | [[Image:Evangiles_d'Echternach.jpg|right|thumb| | + | [[Image:Evangiles_d'Echternach.jpg|right|thumb|200 px|Gospel of Echternach]] |

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. | 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. | ||

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+ | ==Knot Tables== | ||

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+ | 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. | ||

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+ | [[Image:Knots-3-7cross.png]] | ||

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+ | The original image can be found at The knot Atlas page.<ref>http://katlas.math.toronto.edu/wiki/The_Rolfsen_Knot_Table The Knot atlas </ref>. On this site you can click on the knots to obtain more information. | ||

## Revision as of 10:33, 10 May 2007

Relevant examples from Escher's work:

## 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.

## 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.^{[1]}. On this site you can click on the knots to obtain more information.

## References

- ↑ http://katlas.math.toronto.edu/wiki/The_Rolfsen_Knot_Table The Knot atlas