Covering Belt Bodies by Smaller Homothetical Copies
نویسندگان
چکیده
Let b(K) denote the minimal number of smaller homothetical copies of a convex body K ⊂ R, n ≥ 2, covering K. For the class B of belt bodies, which is dense in the set of all convex bodies (in the Hausdorff metric), 3 · 2 is known to be an upper bound on b(K) if K is different from a parallelotope. We will show that (except for all parallelotopes and two particular cases, each satisfying b(K) = 3 · 2) within B this bound can be improved to 5 · 2.
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