The densest packing of 19 congruent circles in a circle (Q1282296)
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scientific article; zbMATH DE number 1270430
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The densest packing of 19 congruent circles in a circle |
scientific article; zbMATH DE number 1270430 |
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The densest packing of 19 congruent circles in a circle (English)
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6 December 1999
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It is proved that the densest packing of 19 congruent circles in a circle is the easy conjectured one: a circle in the center, six touching it around and twelve still around as vertices of a regular dodecagon. The proof uses a Bateman-Erdős approach (originally designed for finding the Besicovitch number \(\beta_2=19\)) and author's useful geometrical lemma together with the known optimality results for packing 7, 8, 9, and 10 circles.
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packing
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density
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densest circle packing
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