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In finite geometry a Desarguesian plane, named after Gérard Desargues, is a plane in which Desargues' theorem holds. The ordinary real projective plane is a Desarguesian plane. More generally any projective plane over a division ring is Desarguesian, and conversely Hilbert showed that any Desarguesan projective plane is the projective plane over some division ring. The division ring is commutative if and only if the projective plane satisfies Pappus's hexagon theorem. In particular all finite Desarguesian planes satisfy Pappus's theorem, but there are some infinite ones that do not. There are many examples of non-Desarguesian planes where Desargues's theorem does not hold, such as the Moulton plane. This geometry-related article is a stub. You can help Wikipedia by expanding it. v • d • e References Ch. Weibel: Survey of Nondesarguesian planes