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ISSN : 1226-0657

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Vol.4 No.2

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ON THE OPTIMAL COVERING OF EQUAL METRIC BALLS IN A SPHERE

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.2, pp.137-144
Cho, Min-Shik (Department of Mathematics Education, Korea National University of Education)
Cho, Min-Shik. (1997). ON THE OPTIMAL COVERING OF EQUAL METRIC BALLS IN A SPHERE. 한국수학교육학회지시리즈B:순수및응용수학, 4(2), 137-144.

Abstract

In this paper we consider covering problems in spherical geometry. Let <TEX>$cov_q{S_1}^n$</TEX> be the smallest radius of q equal metric balls that cover n-dimensional unit sphere <TEX>${S_1}^n$</TEX>. We show that <TEX>$cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$</TEX> and <TEX>$\pi-arccos(\frac{-1}{n+1})$</TEX> for q = n ＋ 2. The configuration of centers of balls realizing <TEX>$cov_q{S_1}^n$</TEX> are established, simultaneously. Moreover, some properties of <TEX>$cov_{q}$</TEX>X for the compact metric space X, in general, are proved.

keywords
Spherical Geometry, Covering Radii, Covering Problems

한국수학교육학회지시리즈B:순수및응용수학

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