A282279 Decimal expansion of minimal radius of a circle that contains 12 non-overlapping unit disks.

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

Offset: 1

Author

Matthew House, Feb 10 2017

Keywords

• nonn
• cons

Examples

			4.029601930116183497482741041263349896...
		

Links

• Matthew House, Table of n, a(n) for n = 1..10000
• F. Fodor, The densest packing of 12 congruent circles in a circle, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 41 (2000), No. 2, 401-409.

Programs

Mathematica

r = Root[#^5 - 3 #^4 + 7 #^2 - 15 # + 9 &, 3];
N[1 + 2 r/Sqrt[3], 20]

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

Formula

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...