The main result of this paper is the proof of a conjecture of L. Fejes T6th saying that the incircles of the Archimedean tiling (4, 8, 8) form a solid packing. To achieve this a new technique, the… (More)

A family of disks is said to have the property T (k) if any k members of the family have a common line transversal. We call a family of unit diameter disks t-disjoint if the distances between the… (More)

In the present paper lattice packings of open unit discs are considered in the Euclidean plane. Usually, efficiency of a packing is measured by its density, which in case of lattice packings is the… (More)

In this paper we consider coverings of the plane by circles of two different sizes. We establish a sufficient condition for such a covering to be solid in the sense of L. Fejes Tóth [6]. As an… (More)

Kershner proved in 1939 that the density of a covering of the plane by congruent circles is at least 2π/ √ 27 [3]. In 1950 L. Fejes Tóth [2] extended this result showing that the same density bound… (More)