Maximin Distance for n Points in a Unit Square or a Unit Circle
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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
Given n points inside a unit square (circle), let dn(cn) denote the maximum value of the minimum distance between any two of the n points. The problem of determining dn(cn) and identifying the configuration of that yields dn(cn) 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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