Geodesic
A Packing Inequality for Compact Convex Subsets of the Plane
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 745-752

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a compact metric space. By a packing in X we mean a subset S ⊆ X such that, for x, y ∈ S with x ≠ y, the distance d(x, y) ≥ 1. Since X is compact, any packing of X is finite. In fact, the set of numbers{card(S): S is a packing in X}is bounded. The cardinality of the largest packing in X will be called the packing number of X and will be denoted by ρ(X). If A(X) and P(X) denote the area and perimeter, respectively, of a compact convex subset X of the plane, then a special case of a result conjectured by H. Zassenhaus [6] and proved by N. Oler [l] is the following. 
Folkman, J. H.; Graham, R. L. A Packing Inequality for Compact Convex Subsets of the Plane. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 745-752. doi: 10.4153/CMB-1969-096-7
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