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A179296
Decimal expansion of circumradius of a regular dodecahedron with edge length 1.
10
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
REFERENCES
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง12.4 Theorems and Formulas (Solid Geometry), p. 451.
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[(Sqrt[3]+Sqrt[15])/4, 10, 175][[1]]
PROG
(PARI) (1+sqrt(5))*sqrt(3)/4 \\ Stefano Spezia, Jan 27 2025
CROSSREFS
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved