The distinct distances problem is a famous problem posed by Erdős in 1946. It asks: how few distinct distances can be determined by a set of n points in the plane? At first, this simple question sounds more like a riddle than a serious mathematical problem. However, it turned out to be extremely difficult and led to the development of a deep theory.

​

In the polymath REU project, we will explore the behavior of the distinct distances problem under different distance norms. There have been some works in this direction, but there still seems to be a lot of unexplored territory to study. While the problem is in combinatorial geometry, one direction for studying the problem involves group theory.

​