In mathematics, a non-Desarguesian plane, named after Gérard Desargues, is a projective plane that does not satisfy Desargues's theorem, or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is valid in all projective spaces of dimension not 2, that is, all the classical projective geometries over a field (or division ring), but Hilbert found that some projective planes do not satisfy it. Understanding of these examples is not complete, in the current state of knowledge.
Other articles related to "planes, plane":
... Lenz classified projective planes in 1954 and this was refined by A ... based on the types of point–line transtitivity permitted by the collineation group of the plane and is known as the Lenz–Barlotti classification of ... known existence results (for both collineation groups and planes having such a collineation group) in both the finite and infinite cases appears on page 126 ...
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“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
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