Two results about points, lines and planes
type: Item
instance of: scholarly article
title: Two results about points, lines and planes
zbMATH Open document ID: 0597.52007
DOI: 10.1016/0012-365X(86)90014-2
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The results are: Given n points in \(E_ 3\) not all on a plane and determining \(\ell\) lines and p planes, it holds a) \(\ell^ 2\geq cnp\), \(c>0\), b) if not all points are contained in two skew lines, then there is a point (of the original ones) that is incident with at least \(b\ell\) of the (original) planes, where \(b>0\). - The results are related to two conjectures on the objects investigated. [Cf. \textit{J. Beck}, Combinatorica 3, 281-297 (1983; Zbl 0533.52004) and the author, Geom. Dedicata 10, 317-321 (1981; Zbl 0474.52013)].
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 3962626
zbMATH Keywords: points-lines-planes conjecture
zbMATH Keywords: n points in Euclidean space
zbMATH Keywords: combinatorial geometry
zbMATH Keywords: arrangement of points
author: George B. Purdy
reviewed by: Ernest Jucovič
MaRDI profile type: Publication
cites work: On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
cites work: Extremal problems in discrete geometry
cites work: Q4111952
cites work: Q3689794
cites work: A proof of a consequence of Dirac's conjecture
description: scientific article; zbMATH DE number 3962626