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In mathematics, a non-Desarguesian plane, named after Girard Desargues, is a projective plane that does not satisfy Desargues' 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,〔Desargues' theorem is vacuously true in dimension 1, it is only problematic in dimension 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. ==Examples== Several examples are also finite. For a finite projective plane, the ''order'' is one less than the number of points on a line (a constant for every line). Some of the 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.〔see for descriptions of all four planes of order 9.〕 *Hughes planes. *Moufang planes over alternative division rings that are not associative, such as the projective plane over the octonions. *Hall planes. *André planes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Non-Desarguesian plane」の詳細全文を読む スポンサード リンク
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