A102769 - OEIS

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

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OFFSET

1,1

COMMENTS

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

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.

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

EXAMPLE

7.663118960624631968716053920...

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A019859 A188736 A265304 * A031348 A247674 A109696

Adjacent sequences: A102766 A102767 A102768 * A102770 A102771 A102772

KEYWORD

nonn,cons,easy,changed

AUTHOR

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

STATUS

approved