Protecting regular polygons
The protecting number of a convex body \(K\) is defined. This is the minimum number of non-overlapping congruent copies of \(K\) so that they can touch \(K\) and any other congruent copy of \(K\) can not touch \(K\) without overlapping each other. The authors prove the following theorems. Theorem 1. The protecting number of any regular polygon is not greater than four. Theorem 2. The protecting number of the square is four. Theorem 3. The protecting number of the regular \(6n\)-gon is three for all positive integers \(n\).
scientific article; zbMATH DE number 1505611