A One-Page Solution of a Problem of Erdos and Purdy

Rom Pinchasi; Alexandr Polyanskii

doi:10.1007/s00454-019-00139-1

A One-Page Solution of a Problem of Erdos and Purdy

Rom Pinchasi, Alexandr Polyanskii

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

The following theorem was conjectured by Erdős and Purdy: Let P be a set of n> 4 points in general position in the plane. Suppose that R is a set of points disjoint from P such that every line determined by P passes through a point in R. Then | R| ≥ n. In this paper we give a very elegant and elementary proof of this, being a very good candidate for the “book proof” of this conjecture.

Original language	English
Pages (from-to)	382-385
Number of pages	4
Journal	Discrete and Computational Geometry
Volume	64
Issue number	2
DOIs	https://doi.org/10.1007/s00454-019-00139-1
State	Published - 1 Sep 2020

Keywords

Collinear triples
Lines
Points

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-019-00139-1

Cite this

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KW - Lines

KW - Points

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ER -

A One-Page Solution of a Problem of Erdos and Purdy

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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