= Szemerédi–Trotter theorem for unit circles
{c}
{title2=$I(P,\mathcal C)\lesssim |P|^{2/3}|\mathcal C|^{2/3}+|P|+|\mathcal C|$}
For distinct equal-radius circles and a finite point set in the real plane, <incidences between points and curves> satisfy $I(P,\mathcal C)=O(|P|^{2/3}|\mathcal C|^{2/3}+|P|+|\mathcal C|)$. Scaling the plane reduces any common positive radius to one. The constant is universal. The fixed-radius condition bounds the number of circles through two prescribed distinct points by two.
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