An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
Let \(A\) be a convex body in Euclidean space \(\mathbb E^n.\) Let \(H(A)\) be the smallest number of homothetic ``reduced copies'' of \(A\) by which it is possible to cover the whole of \(A.\) The conjecture of Hadwiger is \(H(A) \leqslant 2^n\) [\textit{H.~Hadwiger}, Ungelöste Probleme. 20, Elem. Math. 12, 121 (1957)]. The author proves that \(H(A) \leqslant 16,\) for \(n=3.\)
covering convex body by smaller homothetic copies
scientific article; zbMATH DE number 1334360