Harborth, Heiko; Mengersen, Ingrid Point sets with many unit circles. (English) Zbl 0638.52005 Discrete Math. 60, 193-197 (1986). Let f(n) denote the largest integer for which there are n points in the Euclidean plane with the property that there are f(n) distinct circles with the same radii passing through at least 3 of the n points. The authors establish \(f(3)=1\), \(f(4)=f(5)=4\), \(f(6)=8\), \(f(7)=12\), and announce that \(f(8)=16\). Reviewer: A.Cohen MSC: 52A37 Other problems of combinatorial convexity 52A40 Inequalities and extremum problems involving convexity in convex geometry Keywords:discrete geometry; combinatorial geometry; Euclidean plane PDF BibTeX XML Cite \textit{H. Harborth} and \textit{I. Mengersen}, Discrete Math. 60, 193--197 (1986; Zbl 0638.52005) Full Text: DOI References: [1] Elekes, G., \(n\) points in the plane can determine \(n^{32}\) unit circles, Combinatorica, 4, 131 (1984) · Zbl 0561.52009 [2] Erdös, P., On some of my conjectures in Number Theory and Combinatorics, Congressus Numerantium, 39, 3-20 (1983) [3] Harborth, H., Einheitskreise in ebenen Punktmengen, (3. Kolloquium über Diskrete Geometrie (1985), Institut für Mathematik der Universität Salzburg), 163-168 · Zbl 0572.52020 [4] Moser, W.; Pach, J., Research Problems in Discrete Geometry (1984), problem 25. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.