**
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: ffodor@tntech.edu

**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.

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2000 ELibM for
the EMIS Electronic Edition
*