Distinct-distance set
= Distinct-distance set
{title2=$\Delta(P)=\{|p-q|:p,q\in P\}$}
For a finite planar point set $P$, its <distinct-distance set> is $\Delta(P)=\{|p-q|:p,q\in P\}$. It includes zero for nonempty $P$. Its cardinality measures how many different distances the configuration determines. Ordered point pairs can be grouped according to their distance, which relates the problem to <incidences between points and curves>.