Geodesic
On Packings of Unequal Spheres in Rn
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 967-969

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

Suppose that a sequence of spheres is packed in order of decreasing diameters into the unit cube In of Rn . In recent work (2), I have shown that for n = 2, there exist positive constants K2, s ( = 0.97) such that the area of has an asymptotic lower bound K2(d(Sm))s . Although the methods used were complicated and possibly only viable in two dimensions, it is intuitively clear that such a result should also be true in higher dimensions. 
Larman, D. G. On Packings of Unequal Spheres in Rn. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 967-969. doi: 10.4153/CJM-1968-094-5
@article{10_4153_CJM_1968_094_5,
     author = {Larman, D. G.},
     title = {On {Packings} of {Unequal} {Spheres} in {Rn}},
     journal = {Canadian journal of mathematics},
     pages = {967--969},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-094-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-094-5/}
}
TY  - JOUR
AU  - Larman, D. G.
TI  - On Packings of Unequal Spheres in Rn
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 967
EP  - 969
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-094-5/
DO  - 10.4153/CJM-1968-094-5
ID  - 10_4153_CJM_1968_094_5
ER  - 
%0 Journal Article
%A Larman, D. G.
%T On Packings of Unequal Spheres in Rn
%J Canadian journal of mathematics
%D 1968
%P 967-969
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-094-5/
%R 10.4153/CJM-1968-094-5
%F 10_4153_CJM_1968_094_5

[1] 1. Gilbert, E. N., Randomly packed and solidly packed spheres, Can. J. Math. 16 (1964), 286–298. Google Scholar

[2] 2. Larman, D. G., An asymptotic bound for the residual area ofa packing of discs, Proc. Cambridge Philos. Soc. 62 (1966), 699–704. Google Scholar

[3] 3. Larman, D. G., On the Besicovitch dimension of the residual set of arbitrarily packed disks in the plane, J. London Math. Soc. 18 (1967), 292–302. Google Scholar

[4] 4. Larman, D. G., On the exponent of convergence of a packing of spheres, Mathematika 18 (1966), 57–59. Google Scholar

[5] 5. Larman, D. G., A noie on tfoe Besicovitch dimension of the closest packing of spheres in Rn, Proc. Cambridge Philos. Soc. 18 (1966), 193–195. Google Scholar

[6] 6. Melzak, Z. A., Infinite packings of disks, Can. J. Math. 18 (1966), 838–852. Google Scholar

Cité par Sources :