Affine Geometry - History

History

In 1748, Euler introduced the term affine (Latin affinis, "related") in his book Introductio in analysin infinitorum (chapter XVII). In 1827, August Möbius wrote on affine geometry in his Der barycentrische Calcul (chapter 3).

After Felix Klein's Erlangen program, affine geometry was recognized as a generalization of Euclidean geometry.

In 1912, Edwin B. Wilson and Gilbert N. Lewis developed an affine geometry to express the special theory of relativity.

In 1918, Hermann Weyl referred to affine geometry for his text Space, Time, Matter. He uses affine geometry to introduce vector addition and subtraction at the earliest stages of his development of mathematical physics. Later, E. T. Whittaker wrote:

Weyl's geometry is interesting historically as having been the first of the affine geometries to be worked out in detail: it is based on a special type of parallel transport worldlines of light-signals in four-dimensional space-time. A short element of one of these world-lines may be called a null-vector; then the parallel transport in question is such that it carries any null-vector at one point into the position of a null-vector at a neighboring point.

In 1984, "the affine plane associated to the Lorentzian vector space L2 " was described by Graciela Birman and Katsumi Nomizu in an article entitled "Trigonometry in Lorentzian geometry".