New analysis of the sphere covering problems and optimal polytope approximation of convex bodies
A connection between sphere covering problems, optimal polytope approximation of convex bodies and linear approximation of the function \(\| x\| ^2\) is demonstrated. A new proof lower bound for the thickness in the sphere covering problem derived by \textit{H. S. M. Coxeter, L. Few} and \textit{C. A. Rogers} [Mathematika, Lond. 6, 147--157 (1959; Zbl 0094.35301)] is given. Furthermore an important constant in the optimal polytope approximation of convex bodies is estimated.
scientific article; zbMATH DE number 2165390
scientific article