- The unit distance problem in the plane asks for the maximum number $U(n)$ of unit distances which can be obtained by $n$ points.
- For $k$ unit circles and $m$ points in the plane, $I(k,m)$ counts the number of point-circle incidences.
Now, in Matousek's Discrete Geometry book, he claims that $U(n) \leq \frac{1}{2} I(n,n)$, but my questions is shouldn't it be $U(n) \leq \frac{1}{2} I(n,2n)$, since any two circles possibly intersect in two points?