Generalizations of the shadow problem

• Date: 2016
• Main Authors: Zelinskii, Yu. B., Stefanchuk, M. V., Зелінський, Ю. Б., Стефанчук, М. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1876
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 th...