2 problems

Weak unit distance conjecture. For every $\varepsilon>0$, there exists a constant $C_\varepsilon>0$ such that every finite point set $P\subseteq\mathbb R^2$ determines at most

Let $N$ points be given in the Euclidean plane, and let a unit distance mean a pair of points whose Euclidean distance is $1$. The unit distance conjecture. The number of unit dist…