Abstract
Bambah and Rogers proved that the area of a convex domain in the plane which can be covered byn translates of a given centrally symmetric convex domainC is at most (n−1)h(C)+a(C), whereh(C) denotes the area of the largest hexagon contained inC anda(C) stands for the area ofC. An improvement with a term of magnitude √n is given here. Our estimate implies that ifC is not a parallelogram, then any covering of any convex domain by at least 26 translates ofC is less economic than the thinnest covering of the whole plane by translates ofC.
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Tóth, G.F. Finite coverings by translates of centrally symmetric convex domains. Discrete Comput Geom 2, 353–363 (1987). https://doi.org/10.1007/BF02187889
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DOI: https://doi.org/10.1007/BF02187889