A fractal-like configuration of point-line pairs for the minimal distance problem

Alexander Logunov, Dmitrii Zakharov

We show that for every $n\in \mathbb{N}$ there is a collection of points $p_1,\dots ,p_n$ and lines ${\ell }_1,\dots ,{\ell }_n$ in the unit square such that for any $i$ we have $p_i…