Many unit distances requires many directions
Gabriel Currier, József Solymosi · arXiv (Cornell University) · 2025
In this note, we show that in planar pointsets determining many unit distances, these unit distances must span many directions. Specifically, we show that a set of $n$ points can determine only $o(n^{4/3})$ unit distances from a set of at most $O(n^{1/3})$ directions.