# Desarguesian

### Some articles on desarguesian:

Non-Desarguesian Plane - Examples
... Known examples of non-Desarguesian planes include The Moulton plane ... Every projective plane of order at most 8 is Desarguesian, but there are three non-Desarguesian examples of order 9, each with 91 points and 91 lines ...
Moufang Plane
... Every Desarguesian plane is a Moufang plane, and (as a consequence of the Artin–Zorn theorem) every finite Moufang plane is Desarguesian, but some infinite Moufang planes are non-Desarguesian planes ...
Projective Plane - Vector Space Construction - Desargues' Theorem and Desarguesian Planes
... These planes are called Desarguesian planes, named after Gérard Desargues ... projective plane and the projective plane of order 3 given above are examples of Desarguesian projective planes ... The PG(2,K) notation is reserved for the Desarguesian planes ...
Intersection Theorem - Famous Examples
... The projective plane is then called desarguesian ... A theorem of Amitsur and Bergman states that, in the context of desarguesian projective planes, for every intersection theorem there is a rational identity such that the plane P satisfies the ... Pappus's hexagon theorem holds in a desarguesian projective plane if and only if D is a field it corresponds to the identity ...
Desargues' Theorem - Relation To Pappus' Theorem
... converse of this result is not true, that is, not all Desarguesian planes are Pappian ... (a division ring that is not a field) would therefore be Desarguesian but not Pappian ... states that all finite division rings are fields, all finite Desarguesian planes are Pappian ...