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Densest packing of translates of the union of two circles. (English) Zbl 0606.52004
Let $d(u)$ (resp. $\bar d(u))$ denote the density of the densest packing (resp. lattice packing) of translates of the domain u. An open conjecture is that if u is the union of two convex domains having a point in common, then $d(u)=\bar d(u)$. The author proves this in the case where u is the union of two unit-radius circular discs whose centers have distance at most 2. The paper closes with two conjectures --- one for lattice packings of translates of unions of unit discs, the other for packings of congruent copies of a domain.
Reviewer: W.Moser
MSC:
52C17Packing and covering in $n$ dimensions (discrete geometry)
52A40Inequalities and extremum problems (convex geometry)
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References:
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