A051658 - OEIS

%I #21 Aug 26 2020 09:32:17

%S 4,5,7,12,12,13,14,20,24,21,20,25,25,32,36,40,34,38,37,44,39,43,56,56,

%T 60,56,55,57,65,65,55,63,65,80,80,84,77,77,80,85,100,90,85,82,94,91,

%U 94,111,120,100,97,105,110,115,113,119,113

%N Experimental values for maximal number of contacts between equal circles and the box that are packed into a square.

%D H. T. Croft, K. J. Falconer and R. K. Guy: Unsolved problems in geometry, Springer, New York, 1991.

%H D. Boll, <a href="https://web.archive.org/web/20030211053857/http://www.frii.com/~dboll/packing.html">Optimal Packing Of Circles And Spheres</a>

%H L. G. Casado, I. García, P. G. Szabó, and T. Csendes, <a href="http://www.inf.u-szeged.hu/~pszabo/Pub/18pack2.pdf">Packing Equal Circles in a Square II. - New Results for up to 100 Circles Using the TAMSASS-PECS Algorithm</a>, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 207-224.

%H E. Friedman, <a href="https://erich-friedman.github.io/packing/index.html">Erich's Packing Center</a>

%H C. D. Maranas, C. A. Floudas and P. M. Pardalos, <a href="https://doi.org/10.1016/0012-365x(93)e0230-2">New results in the packing of equal circles in a square</a>, Discrete Mathematics 142 (1995), p. 287-293.

%H K. J. Nurmela and Patric R. J. Östergård, <a href="https://doi.org/10.1007/PL00009306">Packing up to 50 equal circles in a square</a>, Discrete Comput. Geom. 18 (1997) 1, p. 111-120.

%H E. Specht, <a href="http://www.packomania.com/">www.packomania.com</a>

%H P. G. Szabó, <a href="https://web.archive.org/web/20071213183047/http://www.inf.u-szeged.hu/~pszabo/Pack.html">Packing up to 100 circles in a square</a>.

%H P. G. Szabó, T. Csendes, L. G. Casado, and I. García, <a href="http://www.inf.u-szeged.hu/~pszabo/Pub/17pack1.pdf">Packing Equal Circles in a Square I. - Problem Setting and Bounds for Optimal Solutions</a>, Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 191-206.

%K nonn

%O 1,1

%A Eckard Specht (eckard.specht(AT)physik.uni-magdeburg.de)

%E I do not know how many of these values have been rigorously proved. - _N. J. A. Sloane_