Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 44, No. 2, pp. 431440 (2003) 

The densest packing of 13 congruent circles in a circleFerenc FodorFeherviz u. 26, IV/13, H2000 Szentendre, HungaryAbstract: 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 Full text of the article:
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