On an Application of Guth–Katz Theorem
Alex Iosevich, Oliver Roche‐Newton, Misha Rudnev · Mathematical Research Letters · 2011
We prove that for some universal c, a non-collinear set of N > 1 c points in the Euclidean plane determines at least c N log N distinct areas of triangles with one vertex at the origin, as well as at least c N log N distinct dot products.This in particular implies a sum-product bound