Many Antipodal Pairs Force Many Neighboring Pairs

Gábor Damásdi, Laurentiu Ploscaru

Let $X=\{x_1,\dots ,x_n\}\subset {\mathbb{R}}^2$ be a finite set of points of diameter at most $1$. It is natural to expect that if many pairs $(x_i,x_j)$ lie at distance close to $1$…