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- W2086762015 abstract "In non-commutative projective geometry there exist Pappus' configurations whose diagonal points are not collinear. In this paper, we consider two lines r,s in a projective plane and the points A,B on r,A′,B′,C′ on s, and we investigate which points X on r lead to collinear diagonal points in the corresponding Pappus' configuration. A geometric interpretation of this result is given, showing that these are exactly all the fixed points of a projectivity of the line r. Finally, we show that the system of fixed points of a large class of projectivities of the line r may be considered as the set of points X on r such that the diagonal points of a suitable Pappus' configuration defined by X and other points, are collinear." @default.
- W2086762015 created "2016-06-24" @default.
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- W2086762015 date "2001-07-01" @default.
- W2086762015 modified "2023-09-30" @default.
- W2086762015 title "On Pappus' configuration in non-commutative projective geometry" @default.
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- W2086762015 doi "https://doi.org/10.1016/s0024-3795(01)00287-7" @default.
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