Radial Points in the Plane

János Pach, Micha Sharir

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)855-863
Number of pages9
JournalEuropean Journal of Combinatorics
Issue number6
StatePublished - Aug 2001


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