Thinnest Covering of the Euclidean Plane with Incongruent Circles

In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the gener...

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Autor principal:	Dorninger Dietmar
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	circular discs covering of the plane minimum density conjecture of l. fejes tóth and j. molnar upper and lower bounds Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/7e15c90564c74df4b50bffc4d661bd3d
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id	oai:doaj.org-article:7e15c90564c74df4b50bffc4d661bd3d
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spelling	oai:doaj.org-article:7e15c90564c74df4b50bffc4d661bd3d2021-12-05T14:10:38ZThinnest Covering of the Euclidean Plane with Incongruent Circles2299-327410.1515/agms-2017-0002https://doaj.org/article/7e15c90564c74df4b50bffc4d661bd3d2017-04-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0002https://doaj.org/toc/2299-3274In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.Dorninger DietmarDe Gruyterarticlecircular discscovering of the planeminimum densityconjecture of l. fejes tóth and j. molnarupper and lower boundsAnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 40-46 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	circular discs covering of the plane minimum density conjecture of l. fejes tóth and j. molnar upper and lower bounds Analysis QA299.6-433
spellingShingle	circular discs covering of the plane minimum density conjecture of l. fejes tóth and j. molnar upper and lower bounds Analysis QA299.6-433 Dorninger Dietmar Thinnest Covering of the Euclidean Plane with Incongruent Circles
description	In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.
format	article
author	Dorninger Dietmar
author_facet	Dorninger Dietmar
author_sort	Dorninger Dietmar
title	Thinnest Covering of the Euclidean Plane with Incongruent Circles
title_short	Thinnest Covering of the Euclidean Plane with Incongruent Circles
title_full	Thinnest Covering of the Euclidean Plane with Incongruent Circles
title_fullStr	Thinnest Covering of the Euclidean Plane with Incongruent Circles
title_full_unstemmed	Thinnest Covering of the Euclidean Plane with Incongruent Circles
title_sort	thinnest covering of the euclidean plane with incongruent circles
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/7e15c90564c74df4b50bffc4d661bd3d
work_keys_str_mv	AT dorningerdietmar thinnestcoveringoftheeuclideanplanewithincongruentcircles
_version_	1718371847612923904

Thinnest Covering of the Euclidean Plane with Incongruent Circles

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