Eppstein's bound on intersecting triangles revisited

Understand

Let S be a set of n points in the plane, and let T be a set of m triangles with vertices in S.

• Then there exists a point in the plane contained in Omega(m^3 / (n^6 log^2 n)) triangles of T.
• Eppstein (1993) gave a proof of this claim, but there is a problem with his proof.
• Here we provide a correct proof by slightly modifying Eppstein's argument.