Thinnest Covering of the Euclidean Plane with Incongruent Circles

Dietmar Dorninger

Analysis and Geometry in Metric Spaces (2017)

  • Volume: 5, Issue: 1, page 40-46
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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Dietmar Dorninger. "Thinnest Covering of the Euclidean Plane with Incongruent Circles." Analysis and Geometry in Metric Spaces 5.1 (2017): 40-46. <http://eudml.org/doc/288062>.

@article{DietmarDorninger2017,
abstract = {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.},
author = {Dietmar Dorninger},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {circular discs; covering of the plane; minimum density; conjecture of L. Fejes Tóth and J. Molnar; upper and lower bounds},
language = {eng},
number = {1},
pages = {40-46},
title = {Thinnest Covering of the Euclidean Plane with Incongruent Circles},
url = {http://eudml.org/doc/288062},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Dietmar Dorninger
TI - Thinnest Covering of the Euclidean Plane with Incongruent Circles
JO - Analysis and Geometry in Metric Spaces
PY - 2017
VL - 5
IS - 1
SP - 40
EP - 46
AB - 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.
LA - eng
KW - circular discs; covering of the plane; minimum density; conjecture of L. Fejes Tóth and J. Molnar; upper and lower bounds
UR - http://eudml.org/doc/288062
ER -

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