Knot theory

The trefoil knot is the simplest mathematical knot. It is impossible to untie without breaking the 'rope'.

Knot theory is the study of knots in mathematics. In knot theory, the ends of the rope are attached so that there is no possible way for the knot to be untied. Peter Guthrie Tait was the first person to make charts describing mathematical knots in the 1860s.

Knot Theory Media

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  Examples of different knots including the trivial knot (top left) and the trefoil knot (below it)

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  A knot diagram of the trefoil knot, the simplest non-trivial knot

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  Intricate Celtic knotwork in the 1200-year-old Book of Kells

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  The first knot tabulator, Peter Guthrie Tait

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  This picture illustrates the Reidemeister move of type I. The move appears as one of fundametal proceidures to deform knots without changing their equivalence class in knot theory (matheamtics). This type I move deals with kinks in the string. The picture shows the strings as 3D objects to illustrate the vertical arrangement.

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  frame sliced - left

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  This picture illustrates the Reidemeister move of type II. The move appears as one of fundametal proceidures to deform knots without changing their equivalence class in knot theory (matheamtics). This type II move deals with two portions with no links of the string. The picture shows the strings as 3D objects to illustrate the vertical arrangement.

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  This picture illustrates the Reidemeister move of type III. The move appears as one of fundametal proceidures to deform knots without changing their equivalence class in knot theory (matheamtics). This type III move deals with ertically aligned three portions of the string. The picture shows the strings as 3D objects to illustrate the vertical arrangement.

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  A 3D print depicting the complement of the figure eight knotby François Guéritaud, Saul Schleimer, and Henry Segerman

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  Skein relation for knots

Related pages

• List of knots
• Topology

Further reading

• Richard H. Crowell and Ralph Fox, Introduction to Knot Theory, 1977, ISBN 0-387-90272-4
• Gerhard Burde and Heiner Zieschang, Knots, De Gruyter Studies in Mathematics, 1985, Walter de Gruyter, ISBN 3-11-008675-1
• Louis H. Kauffman, On Knots, 1987, ISBN 0-691-08435-1