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Radial Points in the Plane

✍ Scribed by János Pach; Micha Sharir

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
103 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

A radial point for a finite set P in the plane is a point q ∈ P with the property that each line connecting q to a point of P passes through at least one other element of P. We prove a conjecture of Pinchasi, by showing that the number of radial points for a non-collinear n-element set P is O(n). We also present several extensions of this result, generalizing theorems of Beck, Szemerédi and Trotter, and Elekes on the structure of incidences between points and lines.

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