Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 2, pp. 431-440 (2003)
The densest packing of 13 congruent circles in a circle
Ferenc FodorFeherviz u. 26, IV/13, H-2000 Szentendre, Hungary
Abstract: The densest packings of $n$ congruent circles in a circle are known for $n\leq 12$ and $n=19$. In this article we examine the case of $13$ congruent circles. We show that the optimal configurations are identical to Kravitz's conjecture. We use a technique developed from a method of Bateman and Erdos, which proved fruitful in investigating the cases $n=12$ and $19$.
Keywords: circle packing, density, optimal packing
Classification (MSC2000): 52C15
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Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.