A282279 - OEIS

%I #9 Feb 11 2017 01:32:05

%S 4,0,2,9,6,0,1,9,3,0,1,1,6,1,8,3,4,9,7,4,8,2,7,4,1,0,4,1,2,6,3,3,4,9,

%T 8,9,6,2,9,5,8,0,5,8,3,5,8,8,3,4,2,3,9,5,6,3,4,4,3,4,1,9,3,7,1,0,0,0,

%U 6,6,1,0,4,8,6,5,2,0,4,9,6,3,9,8,6,6,4

%N Decimal expansion of minimal radius of a circle that contains 12 non-overlapping unit disks.

%H Matthew House, <a href="/A282279/b282279.txt">Table of n, a(n) for n = 1..10000</a>

%H F. Fodor, <a href="http://www.emis.de/journals/BAG/vol.41/no.2/9.html">The densest packing of 12 congruent circles in a circle</a>, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 41 (2000), No. 2, 401-409.

%F Set r as the greatest real root of x^5 - 3*x^4 + 7*x^2 - 15*x + 9 = 0. Then, A = 1 + 2*r/sqrt(3) = 4.029601930...

%e 4.029601930116183497482741041263349896...

%t r = Root[#^5 - 3 #^4 + 7 #^2 - 15 # + 9 &, 3];

%t N[1 + 2 r/Sqrt[3], 20]

%o (PARI) r = solve(x=2, 3, x^5 - 3*x^4 + 7*x^2 - 15*x + 9); 1 + 2*r/sqrt(3) \\ _Michel Marcus_, Feb 11 2017

%K nonn,cons

%O 1,1

%A _Matthew House_, Feb 10 2017