|
%I #31 Sep 08 2022 08:46:06
%S 7,7,3,9,2,0,8,8,0,2,1,7,8,7,1,7,2,3,7,6,6,8,9,8,1,9,9,9,7,5,2,3,0,2,
%T 2,7,0,6,2,7,3,9,8,8,1,4,4,8,1,5,8,1,2,5,2,8,2,6,6,9,8,7,5,2,4,4,0,0,
%U 8,9,6,4,4,8,3,8,4,1,0,4,8,6
%N Ideal rectangle side length for packing squares with side 1/n.
%C With one side s_1 = 1/2+1/3 = 5/6, and with area A = s_1*s_2 = sum(n=2,infinity, 1/n^2) = Pi^2/6 - 1 = A013661 - 1, the second side, s_2, can be solved.
%C The current packing record holder is _Marc Paulhus_, who developed a packing algorithm (see Link).
%H G. C. Greubel, <a href="/A233699/b233699.txt">Table of n, a(n) for n = 0..10000</a>
%H M. M. Paulhus, <a href="http://dx.doi.org/10.1006/jcta.1997.2836">An Algorithm for Packing Squares</a>, Journal of Combinatorial Theory,1998, A,82(2), pages 147-157.
%H Pegg Jr, Ed., Wolfram Demonstrations Project, <a href="http://demonstrations.wolfram.com/PackingSquaresWithSide1N/">Packing Squares with Side 1/n</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Basel_problem#Packing_Squares_with_Side_1.2Fn">Packing Squares with Side 1/n</a>
%F Equals (Pi^2-6)/5 = A164102/10 - 6/5.
%e 0.77392088021787172376689819997523022706273988144815812528266987524400896448...
%t RealDigits[(Pi^2-6)/5,10,120][[1]] (* _Harvey P. Dale_, Aug 21 2017 *)
%o (PARI) (Pi^2-6)/5;
%o (Magma) C<i> := ComplexField(); (Pi(C)^2-6)/5 // _G. C. Greubel_, Jan 26 2018
%K nonn,cons
%O 0,1
%A _John W. Nicholson_, Dec 15 2013
|
