Maximin Distance for n Points in a Unit Square or a Unit Circle
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.
Unable to display preview. Download preview PDF.
- 1.Donovan, J.: Packing Circles in Squares and Circles Page, http://home.att.net/~donovanhse/Packing/index.html
- 4.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)Google Scholar