A179296 Decimal expansion of circumradius of a regular dodecahedron with edge length 1.

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

Offset

1,2

Comments

Dodecahedron: A three-dimensional figure with 12 faces, 20 vertices, and 30 edges.

Appears as a coordinate in a degree-7 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 and Don Secrest, Approximate integration formulas for certain spherically symmetric regions, Math. Comp. 17 (82) (1963) 105.

Wikipedia, Dodecahedron.

Wolfram Alpha, Dodecahedron.

Index entries for algebraic numbers, degree 4

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

Equals (sqrt(3)/2) * phi = A010527 * A001622. - Amiram Eldar, Jun 02 2023

Example

1.40125853844407354467667793532206799444393173977549286366084518639135...

Mathematica

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

Crossrefs

Cf. A001622, 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: A141277 A198637 A365094 * A196817 A229987 A343953

Adjacent sequences: A179293 A179294 A179295 * A179297 A179298 A179299

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

Status

approved