A102208 Decimal expansion of the volume of an icosahedron with unit edge length.

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

Offset: 1

Author

Bryan Jacobs (bryanjj(AT)gmail.com), Feb 17 2005

Keywords

• cons
• easy
• nonn

Examples

			2.181694990624912373503822...
		

References

• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 451.

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Icosahedron.
• Wikipedia, Icosahedron - Area and volume.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A001622 (phi), A020829 (regular tetrahedron volume), A131594 (regular octahedron volume), A102769 (regular dodecahedron volume).

Cf. A071402.

Programs

Mathematica

RealDigits[5/12*(3+Sqrt[5]),10, 200][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

PARI

5*(3 + sqrt(5))/12 \\ G. C. Greubel, Jul 06 2017

Formula

Equals 5 * (3 + sqrt(5))/12.

Equals 5*phi^2/6, phi being the golden ratio. - Stanislav Sykora, Nov 23 2013