Distinct distances from three points
Micha Sharir, Jozsef Solymosi

TL;DR
This paper improves the lower bound on the number of distinct distances from three fixed non-collinear points to a set of n points in the plane, advancing understanding in combinatorial geometry.
Contribution
It provides a stronger lower bound of n^{6/11} for the number of distinct distances, improving previous bounds and simplifying the analysis.
Findings
Established a lower bound of n^{6/11} on the number of distinct distances.
Improved upon the previous bound of n^{0.502}.
Simplified the proof technique compared to prior work.
Abstract
Let be three non-collinear points in the plane, and let be a set of other points in the plane. We show that the number of distinct distances between and the points of is , improving the lower bound of Elekes and Szab\'o \cite{ESz} (and considerably simplifying the analysis).
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