

A179296


Decimal expansion of circumradius of a regular dodecahedron with edge length 1.


5



1, 4, 0, 1, 2, 5, 8, 5, 3, 8, 4, 4, 4, 0, 7, 3, 5, 4, 4, 6, 7, 6, 6, 7, 7, 9, 3, 5, 3, 2, 2, 0, 6, 7, 9, 9, 4, 4, 4, 3, 9, 3, 1, 7, 3, 9, 7, 7, 5, 4, 9, 2, 8, 6, 3, 6, 6, 0, 8, 4, 5, 1, 8, 6, 3, 9, 1, 3, 5, 4, 0, 2, 7, 2, 1, 1, 4, 4, 4, 7, 6, 7, 6, 5, 0, 1, 0, 8, 3, 9, 0, 9, 0, 3, 9, 8, 0, 5, 2, 3, 3, 9, 7, 9, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Dodecahedron: A three dimensional figure with 12 faces, 20 vertices, and 30 edges.
Appears as a coordinate in a degree7 quadrature formula on 12 points over the unit circle [Stroud & Secrest].  R. J. Mathar, Oct 12 2011


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10001
A. H. Stroud, D. Secrest, Approximate integration formulas for certain spherically symmetric regions, Math. Comp. 17 (82) (1963) 105
Wikipedia, Dodecahedron
Wolfram alpha, Dodecahedron


FORMULA

Equals (sqrt(3)+sqrt(15))/4 = sqrt((9+3*sqrt(5))/8).
The minimal polynomial is 16*x^4  36*x^2 + 9. [Joerg Arndt, Feb 05 2014]


EXAMPLE

1.40125853844407354467667793532206799444393173977549286366084518639135...


MATHEMATICA

RealDigits[N[(Sqrt[3]+Sqrt[15])/4, 175]]


CROSSREFS

Cf. A102208, A102769, A131595, A179290, A179292, A179294.
Cf. Platonic solids circumradii: A010503 (octahedron), A010527 (cube), A019881 (icosahedron), A187110 (tetrahedron).  Stanislav Sykora, Feb 10 2014
Sequence in context: A071637 A141277 A198637 * A196817 A229987 A307769
Adjacent sequences: A179293 A179294 A179295 * A179297 A179298 A179299


KEYWORD

nonn,cons,easy


AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 09 2010


STATUS

approved



