Einheitskreise in ebenen Punktmengen. (German) Zbl 0572.52020

Harborth, Heiko

Diskrete Geometrie, 3. Kolloq., Salzburg 1985, 163-168 (1985).

[For the entire collection see Zbl 0563.00013.]
Let n points in the plane be given. What is the maximum number f(n) of congruent circles which are determined by non-collinear triples of these points? In a joint paper with Mengersen the author determined \(f(3)=1\), \(f(4)=4\), \(f(5)=4\), \(f(6)=8\) and \(f(7)=12\). In the present article he shows that \(f(8)=16\). The proof is elementary but involved.

Reviewer: P.Gruber

MSC:

52A37	Other problems of combinatorial convexity
52A10	Convex sets in \(2\) dimensions (including convex curves)
52A40	Inequalities and extremum problems involving convexity in convex geometry

Keywords:

arrangement of points; combinatorial problems; congruent circles

Citations:

Zbl 0563.00013