Thinnest Covering of the Euclidean Plane with Incongruent Circles

• Autorzy: Dietmar Dorninger
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

circular discs; covering of the plane; minimum density; conjecture of L. Fejes Tóth and J. Molnar; upper and lower bounds

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 40-46

Daty

wydano

2017-03-01

otrzymano

2015-08-25

zaakceptowano

2017-03-02

online

2017-04-12

Twórcy

autor

Dietmar Dorninger

• Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna,

Identyfikatory

DOI

10.1515/agms-2017-0002