2-bridge knot

In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given by the z-coordinate has only two maxima and two minima as critical points. Equivalently, these are the knots with bridge number 2, the smallest possible bridge number for a nontrivial knot. Every nontrivial knot with up to seven crossings is a 2-bridge knot. The simplest knots with a bridge number of 3 have eight crossings. Of the 1,701,936 knots with up to sixteen crossings, 5,546 are 2-bridge knots.
Other names for 2-bridge knots are rational knots, 4-plats, and. 2-bridge links are defined similarly as above, but each component will have one min and max. 2-bridge knots were classified by Horst Schubert, using the fact that the 2-sheeted branched cover of the 3-sphere over the knot is a lens space.

Schubert normal form

The names rational knot and rational link were coined by John [Horton Conway|John Conway] who defined them as arising from numerator closures of rational tangles.
This definition can be used to give a bijection between the set of 2-bridge links and the set of rational numbers; the rational number associated to a given link is called
the Schubert normal form of the link, and is precisely the fraction associated to the rational tangle whose numerator closure gives the link.