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Deviation of the centroid of a convex figure from the center of the circumscribed disk

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Abstract

The estimateOG/R ≤ const ≈ 0.4278 for the distanceOG between the centroid G of a plane closed convex figure and the centerO of its circumscribed disk of radius R is obtained. It is shown that this estimate is exact.

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Literature cited

  1. B. Gryunbaum, Studies in Combinatorial Geometry and Theory of Convex Bodies [in Russian], Nauka, Moscow (1971).

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  2. A. A. Kosmodem'yanskii, A Course of Theoretical Mechanics [in Russian], Pt. 1, Prosveshchenie, Moscow (1965).

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Authors and Affiliations

  1. Leningrad State University, USSR

    Yu. G. Dutkevich

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  1. Yu. G. Dutkevich
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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 161–164, February, 1976.

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Dutkevich, Y.G. Deviation of the centroid of a convex figure from the center of the circumscribed disk. Mathematical Notes of the Academy of Sciences of the USSR 19, 97–99 (1976). https://doi.org/10.1007/BF01098739

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  • DOI: https://doi.org/10.1007/BF01098739

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