The Packing of Spheres in the Space lp
Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 22-25
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A point x in the real or complex space lpis an infinite sequence,(x1, x2, x3,...) of real or complex numbers such that is convergent. Here p ≥ 1 and we writeThe unit sphere S consists of all points x ε lp for which ¶ x ¶ ≤ 1. The sphere of radius a≥ ≤ 0 and centre y is denoted by Sa(y) and consists of all points x ε lp such that ¶ x - y ¶ ≤ a. The sphere Sa(y) is contained in S if and only if ¶ y ¶≤1 - a, and the two spheres Sa(y) and Sa(z) do not overlap if and only if¶ y- z ¶≥ 2aThe statement that a finite or infinite number of spheres Sa (y) of fixed radius a can be packed in S means that each sphere Sa (y) is contained in S and that no two such spheres overlap.
The Packing of Spheres in the Space lp. Glasgow mathematical journal, Tome 4 (1958) no. 1, pp. 22-25. doi: 10.1017/S2040618500033797
@misc{10_1017_S2040618500033797,
title = {The {Packing} of {Spheres} in the {Space} lp},
journal = {Glasgow mathematical journal},
pages = {22--25},
year = {1958},
volume = {4},
number = {1},
doi = {10.1017/S2040618500033797},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033797/}
}
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[3] 3.Rankin, R. A., On packings of spheres in Hilbert space, Proc. Glasgow Math. Assoc., 2 (1955), 145–146. Google Scholar | DOI
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