Abstract
Given n points inside a unit square (circle), let d n (c n ) denote the maximum value of the minimum distance between any two of the n points. The problem of determining d n (c n ) and identifying the configuration of that yields d n (c n ) has been investigated using geometric methods and computer-aided methods in a number of papers. We investigate the problem using a computer-aided search and arrive at some approximations which improve on earlier results for n=59, 73 and 108 for the unit square, and also for n=70, 73, 75 and 77, ⋯ , 80 for the unit circle. The associated configurations are identified for all the above-mentioned improved results.
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References
Donovan, J.: Packing Circles in Squares and Circles Page, http://home.att.net/~donovanhse/Packing/index.html
Moser, L.: Problem 24 (corrected). Canadian Mathematical Bulletin 3, 78 (1960)
Specht, E.: www.packomania.com, http://www.packomania.com , http://www.packomania.com
Szabó, P.G., Csendes, T., Casado, L.G., García, I.: Equal circles packing in a square I – Problem setting and bounds for optimal solutions. New Trends in Equilibrium Systrems, 1–15 (2000)
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© 2003 Springer-Verlag Berlin Heidelberg
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Akiyama, J., Mochizuki, R., Mutoh, N., Nakamura, G. (2003). Maximin Distance for n Points in a Unit Square or a Unit Circle. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_2
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DOI: https://doi.org/10.1007/978-3-540-44400-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
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