DECOMPOSING THE 2-SPHERE INTO DOMAINS OF SMALLEST POSSIBLE DIAMETER

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Abstract

In the present paper the following sphere decomposition problem is discussed: For a given natural number n what is the smallest possible value σ(d, n) such that S^d can be decomposed into n parts each of (spherical) diameter ≤ σ(d, n)? The author investigates the problem for d = 2 and gives the answer for n < 7 as well as for n = 8 and n = 9. Partial results are given for n = 7, 10 and 12 and for the analogous problem in the plane.

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