# Pasch's theorem

Pasch's theorem Not to be confused with Pasch's axiom regarding a line through a triangle.

In der Geometrie, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch,[1] is a result in plane geometry which cannot be derived from Euclid's postulates.

Inhalt 1 Aussage 2 Siehe auch 3 Anmerkungen 4 Verweise 5 External links Statement The statement is as follows: Pasch's theorem — Given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) und (b, c, d), then it is also true that (a, b, d).[2] [Hier, zum Beispiel, (a, b, c) means that point b lies between points a and c.] See also Ordered geometry Pasch's axiom Notes ^ Pasch 1912 ^ Coxeter (1969, p. 179) states the result in 12.274 but does not refer to it specifically as Pasch's theorem. Referenzen Coxeter, H.S.M. (1969), Introduction to geometry (2und Aufl.), John Wiley und Söhne, ISBN 978-0-471-18283-2, Zbl 0181.48101 Pasch, Moritz (1912) [first edition 1882], Vorlesungen uber neuere Geometrie (auf Deutsch) (2und Aufl.), Leipzig: B.G. Teubner External links Weisstein, Erich W. "Pasch's Theorem". MathWorld. This elementary geometry-related article is a stub. Sie können Wikipedia helfen, indem Sie es erweitern.

Kategorien: Euclidean plane geometryFoundations of geometryOrder theoryTheorems in plane geometryElementary geometry stubs

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