We show the following two results on a set of n points in the plane, thus answering questions posed by ErdÅ‘s and Purdy [11]: 1. The maximum number of triangles of maximum area (or of maximumâ€¦ (More)

In this note we prove two results on the quantitative illumination parameter f (d) of the unit ball of a d-dimensional normed space introduced by K. Bezdek (1992). The first is that f (d) = O(2dd2â€¦ (More)

We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d â‰¥ 4 and nâ€¦ (More)

The famous Fermat-Torricelli problem (in Location Science also called the SteinerWeber problem) asks for the unique point x minimizing the sum of distances to arbitrarily given points x1, . . . ,xnâ€¦ (More)

Hellyâ€™s theorem implies that if S is a finite collection of (positive) homothets of a planar convex body B, any three having non-empty intersection, then S has non-empty intersection. We show thatâ€¦ (More)