In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's postulates. == Statement == The statement is as follows: [Here, for example, (a, b, c) means that point b lies between points a and c.] == Hilbert's use of Pasch's theorem == David Hilbert originally included Pasch's theorem as an axiom in his modern treatment of Euclidean geometry in The Foundations of Geometry (1899).
In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's postulates. == Statement == The statement is as follows: [Here, for example, (a, b, c) means that point b lies between points a and c.] == Hilbert's use of Pasch's theorem == David Hilbert originally included Pasch's theorem as an axiom in his modern treatment of Euclidean geometry in The Foundations of Geometry (1899).
Source: Wikipedia "Pasch's theorem" · CC BY-SA 4.0
Share this article: X · Bluesky