A result about Leisenring points
type: Item
instance of: scholarly article
title: A result about Leisenring points
zbMATH Open document ID: 0789.51003
DOI: 10.1007/BF01226798
author: Maria Pompea Di Melfi
author: Antonio Cossidente
published in: Journal of Geometry
publication date: 1994-02-06T00:00:00Z
review text: Let \(A_ 1\), \(A_ 2\), \(A_ 3\) and \(B_ 1\), \(B_ 2\), \(B_ 3\) be two sets of distinct collinear points on two distinct lines in a projective plane. Let \(P_ 1=A_ 2B_ 3 \cap A_ 3B_ 2\); \(P_ 2=A_ 3B_ 1 \cap A_ 1B_ 3\), \(P_ 3=A_ 1B_ 2 \cap A_ 2B_ 1\). The Pappus condition is that \(P_ 1\), \(P_ 2\), \(P_ 3\) are collinear for all choices of the \(A_ i\), \(B_ i\). Let \(O\) be the intersection of the two lines. Let \(L_ 1=OP_ 1 \cap A_ 1B_ 1\), \(L_ 2=OP_ 2 \cap A_ 2B_ 2\), \(L_ 3=OP_ 3 \cap A_ 3B_ 3\). The Leisenring condition is that \(L_ 1\), \(L_ 2\), \(L_ 3\) are collinear. The authors show that in a Moufang-Anti-Fano plane, the Leisenring condition implies the Pappus condition.
Mathematics Subject Classification ID: 51A20
zbMATH DE Number: 493213
zbMATH Keywords: Moufang-Anti-Fano plane
zbMATH Keywords: Leisenring condition
zbMATH Keywords: Pappus condition
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01226798
OpenAlex ID: W2056002203
description: scientific article; zbMATH DE number 493213