Alexandre-Théophile Vandermonde, Peter Guthrie Tait mathematics |

## Knot theory

- A cord may be wound around itself
- and after its two ends are fused together
- it will stay tied.
- The question arose as to how
- closed loops like this
- were to be related or distinguished.
- To Vandermonde, a knot
- was like the path of a knight in chess
- as it covers the board without repeating.
- To Lord Kelvin, an atom
- was a knot of aether tied to itself,
- which is both interesting and wrong.
- And this got Peter Guthrie Tait
- to classify all possible knots,
- at least up to ten crossings.

## Knottiness

- The minimum number of crossings
- is a particular knot’s knottiness—counted
- after undoing any nugatory crossings.

## Cat’s cradle

- Let me show you how to make
- a manger for feeding cows
- from a loop of string.
- Thread it through
- the fingers of your two hands
- and let me take the string from you.

## Gordian Knot

- To untangle a mess of yarn,
- it is not permissible to cut it.
- However, one reason
- problems remain unsolved
- and poems remain unwritten
- is a desire to obey the rules.

At first evolving separately, knot theory eventually became part of topology, but I must say that it seems a lot more fun working knots than solving problems in topology.

See also in

The book of science:Graph theory—Leonhard EulerTopology—Leonhard Euler, Antoine-Jean Lhuilier, August Ferdinand Möbius, Johann Benedict Listing, Henri PoincaréEuler characteristic—Leonhard EulerReadings on wikipedia:

Other readings: