Problem 104

Given $n$ points in $\mathbb{R}^2$ the number of distinct unit circles containing at least three points is $o(n^2)$ .

Status

Open

No claim settles this problem.

El84: Elekes, G., $n$ points in the plane can determine $n^{3/2}$ unit circles. Combinatorica (1984), 131.
Er75h: Erdős, P., Some problems on elementary geometry. Austral. Math. Soc. Gaz. (1975), 2-3.
Er81d: Erdős, P., Some applications of graph theory and combinatorial methods to number theory and geometry. Algebraic methods in graph theory, Vol. I, II (Szeged, 1978) (1981), 137-148.
Er92e: Erdős, Pál, Some Unsolved problems in Geometry, Number Theory and Combinatorics. Eureka (1992), 44-48.
HaMe86: Harborth, Heiko and Mengersen, Ingrid, Point sets with many unit circles. Discrete Math. (1986), 193-197.