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Packing up to 200 Equal Circles in a Square

In: Models and Algorithms for Global Optimization

Author

Listed:
  • Péter Gábor Szabó

    (University of Szeged)

  • Eckard Specht

    (University of Magdeburg)

Abstract

The Hungarian mathematician Farkas Bolyai (1775–1856) published in his principal work (‘Tentamen’, 1832–33 [Bol04]) a dense regular packing of equal circles in an equilateral triangle (see Fig. 1). He defined an infinite packing series and investigated the limit of vacuitas (in Latin, the gap in the triangle outside the circles). It is interesting that these packings are not always optimal in spite of the fact that they are based on hexagonal grid packings. Bolyai probably was the first author in the mathematical literature who studied the density of a series of packing circles in a bounded shape.

Suggested Citation

  • Péter Gábor Szabó & Eckard Specht, 2007. "Packing up to 200 Equal Circles in a Square," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 141-156, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-36721-7_9
    DOI: 10.1007/978-0-387-36721-7_9
    as

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