On the density of sets of the Euclidean plane avoiding distance 1

Thomas Bellitto, Arnaud Pêcher, Antoine Sédillot

A subset $A\subset {\mathbb{R}}^2$ is said to avoid distance $1$ if: $\forall x,y\in A,{\Vert x-y\Vert }_2\ne 1.$ In this paper we study the number $m_1({\mathbb{R}}^2)$ which is…