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Multiple covering of the plane by circles

Published online by Cambridge University Press:  26 February 2010

W. J. Blundon
W. J. Blundon
Affiliation:
University College, London and Memorial University of Newfoundland.
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Extract

It is well known that the thinnest covering of the plane by equal circles (of radius 1, say) occurs when the centres of the circles are at the points of an equilateral lattice, i.e. a lattice whose fundamental cell consists of two equilateral triangles. The density of thinnest covering is

Type
Research Article
Information
Mathematika , Volume 4 , Issue 1 , June 1957 , pp. 7 - 16
Copyright
Copyright © University College London 1957

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References

page 7 note * For several proofs, see Tóth, L. Fejes, Lagerungen in der Ebene auf der Kugel und im Baum, (Berlin, 1953), Ch. III.CrossRefGoogle Scholar

page 7 note † Without this restriction the problem becomes much more difficult.

page 8 note * |P| denotes the distance OP, and we use an obvious symbolism for vector addition, so that e.g. P—Q = R, where OR is equal and parallel to QP.

page 8 note † Loc. cit., p. 11.