4. Balls and spheres
4.1 The spheres in ...
Title : Spheres in
A sphere Sn–1(x,r) of center x and radius r in the n-dimensional set of all numbers of relative integers (n ≥ 1), provided with the distance induced by the Euclidean distance, can be empty (unlike the corresponding ball Bn(x,r)). Indeed, such a sphere is non-empty if and only if its radius r can be written as the sum of n squares of integers.
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Balls and spheres
Spaces of sequences of scalar numbers
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