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Asymptotic Behavior of Optimal Circle Packings in a Square

  Published:1999-09-01
 Printed: Sep 1999
  • Kari J. Nurmela
  • Patric R. J. Östergård
  • Rainer aus dem Spring
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Abstract

A lower bound on the number of points that can be placed in a square of side $\sigma$ such that no two points are within unit distance from each other is proven. The result is constructive, and the series of packings obtained contains many conjecturally optimal packings.
Keywords: asymptotic bound, circle packing asymptotic bound, circle packing
MSC Classifications: 52C15 show english descriptions Packing and covering in $2$ dimensions [See also 05B40, 11H31] 52C15 - Packing and covering in $2$ dimensions [See also 05B40, 11H31]
 

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