Covering a planar domain with sets of small diameter

A. Heppes

doi:10.1007/s10998-006-0029-9

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 53: Issue 1-2

Covering a planar domain with sets of small diameter

Author:

A. Heppes

A. Heppes Alfréd Rényi Institute of the Hungarian Academy of Sciences Reáltanoda u. 13-15, H-1053 Budapest, Hungary Reáltanoda u. 13-15, H-1053 Budapest, Hungary

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Pages:: 157–168

Online Publication Date:: 15 Feb 2007

Publication Date:: 15 Sep 2006

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10998-006-0029-9

Keywords:: covering; square; triangle; circle; diameter

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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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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)