On system of balls with equal radii generating shadow at a point

Abstract

Problems related to the determination of the minimal number of balls that generate a shadow at a fixed point in the multi-dimensional Euclidean space Rⁿ are considered in the present work. Here, the statement ”a system of balls generate shadow at a point” means that any line passing through the point intersects at least one ball of the system. The minimal number of pairwise-disjoint balls with equal radii in Rⁿ which do not contain a fixed point of the space and generate shadow at the point is indicated in the work.