Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 401-409 (2000)

The Densest Packing of 12 Congruent Circles in a Circle

Ferenc Fodor

Department of Mathematics, Tennessee Technological University, Box 5054, Cookeville, TN 38505, U.S.A., e-mail:

Abstract: The densest packings of $n$ congruent circles in a circle are known for $n\leq 11$ and $n=19$. In this paper we exhibit the densest packing of $12$ congruent circles in a circle. In fact, we show that the optimal configuration is the same as the one Kravitz [A] conjectured. We use a technique developed from a method of Bateman and Erdos [B]. \item{[A]} Kravitz, S.: Packing cylinders into cylindrical containers. Math. Mag. 40 (1967), 65-71. \item{[B]} Bateman, P.; Erdos, P.: Geometrical extrema suggested by a lemma of Besicovitch. Amer. Math. Monthly 58 (1951), 306-314.

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