We prove that any simple polytope (and some non-simple polytopes) in R 3 admits an inscribed regular octahedron.
For convex partitions of a convex body B we prove that we can put a homo-thetic copy of B into each set of the partition so that the sum of homothety coefficients is ≥ 1. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition.
License Agreement: If you don't like this book, please delete it from your computer. In the other case you should buy it on Arseniy Akopyan. Geometry in Figures. This book is a collection of theorems and problems in classical Euclidean geometry formulated in figures. It is intended for advanced high school and undergraduate students, teachers and all who… (More)