The Dirac-Motzkin Problem on Ordinary Lines and the Orchard Problem (Invited Talk)

Abstract

Suppose you have n points in the plane, not all on a line. A famous theorem of Sylvester-Gallai asserts that there is at least one ordinary line, that is to say a line passing through precisely two of the n points. But how many ordinary lines must there be? It turns out that the answer is at least n/2 (if n is even) and roughly 3n/4 (if n is odd), provided… (More)
DOI: 10.4230/LIPIcs.SOCG.2015.405

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