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

Author

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

Keywords

• nonn
• cons
• easy

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

Examples

			1.40125853844407354467667793532206799444393173977549286366084518639135...
		

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

• 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.

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

Programs

Mathematica

RealDigits[(Sqrt[3]+Sqrt[15])/4, 10, 175][[1]]

PARI

(1+sqrt(5))*sqrt(3)/4 \\ Stefano Spezia, Jan 27 2025

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