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

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...

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Bibliographic Details
Published in:Discrete & computational geometry 2020-09, Vol.64 (2), p.382-385
Main Authors: Pinchasi, Rom, Polyanskii, Alexandr
Format: Article
Language:English
Subjects:
Branko Grünbaum Memorial Issue
Combinatorics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-019-00139-1