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Asymptotic Behavior of Optimal Circle Packings in a Square

Published online by Cambridge University Press:  20 November 2018

Kari J. Nurmela ,
Patric R. J. Östergård  and
Rainer aus dem Spring
Kari J. Nurmela
Affiliation:
Department of Computer Science and Engineering Helsinki University of Technology 02015 HUT Finland, email: [email protected]
Patric R. J. Östergård
Affiliation:
Department of Computer Science and Engineering Helsinki University of Technology 02015 HUT Finland, email: [email protected]
Rainer aus dem Spring
Affiliation:
BERA Softwaretechnik GmbH 40699 Erkrath Germany, email: Rainer.adS.BERA [email protected]
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Abstract

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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

52C15asymptotic boundcircle packing
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 380 - 385
Copyright
Copyright © Canadian Mathematical Society 1999

References

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