stylistic:tone
Kinematics

Two types of affine transformation are used in kinematics, both classical and modern. Velocity v is described using length and direction, where length is presumed unbounded. This variety of kinematics, styled as Galilean or Newtonian, uses coordinates of absolute space and time. The shear mapping of a plane with an axis for each represents coordinate change for an observer moving with velocity v in a resting frame of reference.

Finite light speed, first noted by the delay in appearance of the moons of Jupiter, requires a modern kinematics. The method involves rapidity instead of velocity, and substitutes squeeze mapping for the shear mapping used earlier. This affine geometry was developed synthetically in 1912. to express the special theory of relativity.In 1984, "the affine plane associated to the Lorentzian vector space L " was described by Graciela Birman and Katsumi Nomizu in an article entitled "Trigonometry in Lorentzian geometry".