A102769 Decimal expansion of the volume of a dodecahedron with each edge of unit length.

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

Offset: 1

Author

Bryan Jacobs (bryanjj(AT)gmail.com), Feb 10 2005

Keywords

• nonn
• cons
• easy

Comments

Equals 5*phi^3/(2*xi^2), phi being the golden ratio (A001622) and xi its associate (A182007). - Stanislav Sykora, Nov 23 2013

Examples

			7.663118960624631968716053920...
		

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, Dodecahedron.
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A001622 (phi), A182007 (phi associate), A020829 (regular tetrahedron volume), A131594 (regular octahedron volume), A102208 (regular icosahedron volume).

Programs

Maple

evalf((15+7*sqrt(5))/4,100); # Wesley Ivan Hurt, Jan 29 2017

Mathematica

RealDigits[(Sqrt[5]/2)*(GoldenRatio)^4, 10, 50][[1]] (* G. C. Greubel, Jul 06 2017 *)

PARI

(7*sqrt(5)+15)/4 \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals (15 + 7 sqrt(5)) / 4.

Equals (sqrt(5)/2)*(phi)^4, where phi is the golden ratio. - G. C. Greubel, Jul 06 2017