On Menelaus and Ceva 6-figures in Moufang projective planes
type: Item
instance of: scholarly article
title: On Menelaus and Ceva 6-figures in Moufang projective planes
zbMATH Open document ID: 0574.51004
DOI: 10.1007/BF00149369
published in: Geometriae Dedicata
publication date: 1985-01-01T00:00:00Z
review text: Let \(A_ 1,A_ 2,A_ 3\) be non-collinear points of a projective plane, furthermore let \(A''_ i\) be the fourth harmonic point of \(A_ j,A_ k\), and \(A'_ i\) with \(\{i,j,k\}=\{1,2,3\}\), i.e. \(H(A_ jA_ k,A'_ iA''_ i)\). If the plane is desarguesian, then it is known that \(A'_ 1,A'_ 2,A'_ 3\) are collinear iff \(A_ 1A''_ 1,A_ 2A''_ 2,A_ 3A''_ 3\) are concurrent. The authors extend this result to Moufang planes. It is a pity that the authors did not illustrate their proof by figures.
Mathematics Subject Classification ID: 51A20
Mathematics Subject Classification ID: 51A35
zbMATH DE Number: 3917105
zbMATH Keywords: Menelaus 6-figure
zbMATH Keywords: Ceva 6-figure
zbMATH Keywords: projective plane
zbMATH Keywords: Moufang planes
author: Rüstem Kaya
author: Süleyman Çiftçi
reviewed by: Hanfried Lenz
MaRDI profile type: Publication
cites work: On Desarguesian projective planes
cites work: Q3911027
full work available at URL: https://doi.org/10.1007/bf00149369
OpenAlex ID: W1973949482
description: scientific article; zbMATH DE number 3917105