A lower bound for the number of pinned angles determined by a Cartesian product set

TL;DR

This paper establishes a lower bound on the number of distinct angles determined by the Cartesian product of a real set with itself, showing it grows faster than quadratic in the size of the set.

Contribution

It provides a new lower bound for the number of pinned angles determined by Cartesian product sets, advancing understanding in geometric combinatorics.

Findings

Number of angles grows at least as fast as |B|^{2+c}

Established a lower bound for angles from Cartesian products

Enhances bounds in geometric combinatorics

Abstract

We prove that, for any $B \subset \mathbb R$, the Cartesian product set $B \times B$ determines $\Omega(|B|^{2+c})$ distinct angles.