Geodesic
A Three-Fold Non-Lattice Covering
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 29-31

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Let be the density of thinnest k-fold covering of the plane by equal circles (of radius 1, say). Let Dk be the corresponding density when the centres of the circles are at the points of a lattice Λ. It is clear that 
Blundon, W. J. A Three-Fold Non-Lattice Covering. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 29-31. doi: 10.4153/CMB-1977-005-1
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[1] 1. Blundon, W. J., Multiple coverings of the plane by circles, Mathematika 4 (1957), 7-16. Google Scholar

[2] 2. Danzer, L., Drei Beispliele zu Lagerungsproblemen, Arch. Math. 11 (1960), 159-165. Google Scholar

[3] 3. Kershner, R., The number of circles covering a set, Amer. J. Math. 61 (1939), 655-671. Google Scholar

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