Wild knot (nonfiction)

A wild knot.

In the mathematical theory of knots, a wild knot is a knot that is not tame. Wild knots can have pathological behavior.

A knot is tame if it can be "thickened up" -- that is, if there exists an extension to an embedding of the solid torus S 1 × D 2 into the 3-sphere.

A knot is tame if and only if it can be represented as a finite closed polygonal chain.

Smooth knots, for example, are always tame.

In knot theory and 3-manifold theory, often the adjective "tame" is omitted.

Wild knots can be found in some Celtic designs.

Fiction cross-reference

• Crimes against mathematical constants
• Gnomon algorithm

Nonfiction cross-reference

• Mathematics (nonfiction)
• Wild arc (nonfiction)

External links:

• Wild knot @ Wikipedia