Displaying similar documents to “Note to a paper of Bambah, Rogers and Zassenhaus”

Thinnest Covering of the Euclidean Plane with Incongruent Circles

Dietmar Dorninger (2017)

Analysis and Geometry in Metric Spaces

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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...

Covering the plane with sprays

James H. Schmerl (2010)

Fundamenta Mathematicae

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For any three noncollinear points c₀,c₁,c₂ ∈ ℝ², there are sprays S₀,S₁,S₂ centered at c₀,c₁,c₂ that cover ℝ². This improves the result of de la Vega in which c₀,c₁,c₂ were required to be the vertices of an equilateral triangle.