Wild knot explained
into the
3-sphere. A knot is tame if and only if it can be represented as a
finite closed polygonal chain. Every closed curve containing a
wild arc is a wild knot. Knots that are not tame are called
wild and can have
pathological behavior. In knot theory and
3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame.
It has been conjectured that every wild knot has infinitely many quadrisecants.
As well as their mathematical study, wild knots have also been studied for their potential for decorative purposes in Celtic-style ornamental knotwork.
See also
