affine geometry

== English == === Noun === affine geometry (countable and uncountable, plural affine geometries) (geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored. 1940 [McGraw-Hill], E. T. Bell, The Development of Mathematics, 2017 [1992], Dover, page 265, To include affine geometry, Menger (1935) imposed on lattices a reasonable axiom of parallelism. 1953 [Addison-Wesley], Dirk J. Struik, Lectures on Analytic and Projective Geometry, 2014, Dover, page 108, And affine geometry itself can be considered as the geometry of all projective transformations which leave a line invariant. (countable) A geometry that is otherwise Euclidean but disregards lengths and angle sizes. ==== Usage notes ==== Affine geometry is frequently described as what remains of Euclidean geometry when one "forgets" the metric notions of distance and angle. ==== Related terms ==== affine connection affine group affine space affine transformation centro-affine geometry ==== Translations ==== === Further reading === Erlangen program on Wikipedia.Wikipedia Metric space on Wikipedia.Wikipedia Parallel postulate on Wikipedia.Wikipedia Playfair's axiom on Wikipedia.Wikipedia