Geodesic
On the Exponent of an Osculatory Packing
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 355-363

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

Suppose that U is an open set in Euclidean N-space which has a finite volume |U|. A complete packing of U is a sequence of disjoint N-spheres C = {S n } which are contained in U and whose total volume equals that of U. In an osculatory packing, the spheres are chosen recursively so that for all n larger than a certain value m, Sn has the largest radius of all spheres contained in U\(S 1 – ∪ ... ∪ S n-1 –) (S – is the closure of S). An osculatory packing is simple if m = 1. If rn denotes the radius of Sn , the exponent of the packing is defined by: This quantity is of considerable interest since it measures the effectiveness of the packing of U by C. 
Boyd, David W. On the Exponent of an Osculatory Packing. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 355-363. doi: 10.4153/CJM-1971-036-8
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