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## Mehrfache gitterförmige Kreislagerungen in der Ebene

Acta Mathematica Hungarica
Author:
A. Heppes
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## Über Kreis- und Kugelwolken

Acta Mathematica Hungarica
Author:
A. Heppes
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## Covering a planar domain with sets of small diameter

Periodica Mathematica Hungarica
Author:
A. Heppes

## Summary

The problem of covering a circle, a square or a regular triangle with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document} congruent circles of minimum diameter (the {\it circle covering} problem) has been investigated by a number of authors and the smallest diameter has been found for several values of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document} . This paper is devoted to the study of an analogous problem, the {\it diameter covering} problem, in which the shape and congruence of the covering pieces is relaxed and -- invariably -- the maximal diameter of the pieces is minimized. All cases are considered when the solution of the first problem is known and in all but one case the diameter covering problem is solved.

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## Decomposing the 2-Sphere into Domains of Smallest Possible Diameter

Periodica Mathematica Hungarica
Author:
A. Heppes
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## Research Problem

Periodica Mathematica Hungarica
Author:
A. Heppes
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## Expandability radius versus density of a lattice packing

Periodica Mathematica Hungarica
Author:
A. Heppes

## Abstract

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 quotient of the area of the discs and the area of the fundamental domain of the packing. In this paper another measure, the expandability radius is introduced and its relation to the density is studied. The expandability radius is the radius of the largest disc which can be used to substitute a disc of the packing without overlapping the rest of the packing. Lower and upper bounds are given for the density of a lattice packing of given expandability radius for any feasible value. The bounds are sharp and the extremal configurations are also presented. This packing problem is related to a covering problem studied by Bezdek and Kuperberg [BK97].

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## On the determination of probability distributions of more dimensions by their projections

Acta Mathematica Hungarica
Author:
A. Heppes
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## Beweis einer Vermutung von A. Vázsonyi

Acta Mathematica Hungarica
Author:
A. Heppes
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## Packing of Rounded Domains on a Sphere of Constant Curvature

Acta Mathematica Hungarica
Author:
A. Heppes
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## ON THE DENSEST PACKIN OF DISCS OF RADIUS 1 AND .2 -1

Studia Scientiarum Mathematicarum Hungarica
Author:
A. Heppes

The main goal of this paper is to establish the long-sta di g conjecture that in the Euclidea plane no arrangeme t of discs of radius 1 and .2 -1 ca have larger packi g de sitythan that of the set of incircles of the semiregular (Archimedean)tessellation (8, 8, 4)

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