Let $C_{ i}$ ($\,i=1,\ldots ,N\,$) 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 $i=2,\ldots ,N-1\,$, that $M_{ i}$ is set on the perimeter of $C_{ i-1}$, and that each area of the set $(\cup _{ \nu =1}^{ i-1}C_{ \nu })\cap C_{ i}$ becomes maximum. In this paper, for $N = 10$, we found out that the solutions of our sequential covering and the solutions of the Tammes problem were strictly correspondent. Especially, we succeeded to obtain the exact value $r_{ 10}$ for $N = 10$.
Categories: math.MG