Inscribed and circumscribed polyhedra for a convex body and continuous functions on a sphere in Euclidean space
Inscribed and circumscribed polyhedra for a convex body and continuous functions on a sphere in Euclidean space
Two related problems concerning continuous functions on a sphere $S^{n-1}\subset {\mathbb {R}}^n$ are studied, together with the problem of finding a family of polyhedra in ${\mathbb {R}}^n$ one of which is inscribed in (respectively, circumscribed about) a given smooth convex body in ${\mathbb {R}}^n$. In particular, it is proved that, …