2018
Том 70
№ 9

# Generalizations of the shadow problem

Abstract

We solve the shadow problem in the n-dimensional Euclidean space $N^n$ for a family of sets obtained from any convex domain with nonempty interior with the help of parallel translations and homotheties. We determine the number of balls with centers on the sphere, sufficient for giving a shadow in the $n$-dimensional complex (hypercomplex) space.

Citation Example: Stefanchuk M. V., Zelinskii Yu. B. Generalizations of the shadow problem // Ukr. Mat. Zh. - 2016. - 68, № 6. - pp. 757-763.