Packing and Minkowski Covering of Congruent Spherical Caps on a Sphere, II: Cases of N = 10, 11, and 12
Packing and Minkowski Covering of Congruent Spherical Caps on a Sphere, II: Cases of N = 10, 11, and 12
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发表时间：
2007-09
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通讯作者：
Teruhisa Sugimoto;M. Tanemura
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作者：
Teruhisa Sugimoto;M. Tanemura
设 C i (i = 1, ..., N) 为第 i 个角半径为 r 的开球盖，并设 M i 为其圆心，条件是每个球盖内部都不包含另一个球盖的中心。我们考虑 r 的上界 r N ，（不是下界！），在这种情况下，单位球体的整个球面完全被 N 个全等的开球盖覆盖，依次对于 i = 2, ..., N - 1，Mi 设定在 Ci-1 的周长上，并且集合的每个面积 ( � ν =
Let C i (i = 1, ..., N) be the i-th open spherical cap of angular radius r and let M i be its center under the condition that none of the spherical caps contains the center of another one in its interior. We consider the upper bound, r N , (not the lower bound!) of r of the case in which the whole spherical surface of a unit sphere is completely covered with N congruent open spherical caps under the condition, sequentially for i = 2, ..., N - 1, that Mi is set on the perimeter of Ci-1, and that each area of the set ( � ν =