Cross-ratios and 6-figures in some Moufang-Klingenberg planes
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Date
2008
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Belgin Mathematical Soc Triomphe
Abstract
This paper deals with Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers. The definition of cross-ratio is extended to M(A). Also, some properties of cross-ratios and 6-figures that are well-known for Desarguesian planes are investigated in M(A); so we obtain relations between algebraic properties of A and geometric properties of M(A). In particular, we show that pairwise non-neighbour four points of the line g are in harmonic position if and only if they are harmonic, and that p is Menelaus or Ceva 6-figure if and only if r (mu) = - 1 or r (mu) = 1, respectively.
Description
Keywords
Mathematics, 6-figure, Cross-ratio, Local alternative ring, Moufang-klingenberg planes
Citation
Akpınar, A. vd. (2008). "Cross-ratios and 6-figures in some Moufang-Klingenberg planes". Bulletin of the Belgian Mathematical Society - Simon Stevin, 15(1), 49-64.