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A179292
Decimal expansion of radius of inscribed sphere of an icosahedron with radius of circumscribed sphere = 1.
23
7, 9, 4, 6, 5, 4, 4, 7, 2, 2, 9, 1, 7, 6, 6, 1, 2, 2, 9, 5, 5, 5, 3, 0, 9, 2, 8, 3, 2, 7, 5, 9, 4, 0, 4, 2, 0, 2, 6, 5, 9, 0, 5, 8, 8, 3, 0, 9, 2, 6, 4, 8, 0, 1, 7, 5, 4, 9, 5, 5, 7, 7, 5, 0, 0, 8, 4, 3, 8, 6, 4, 4, 9, 7, 1, 7, 3, 7, 1, 1, 6, 7, 9, 3, 0, 2, 7, 2, 9, 9, 4, 8, 4, 8, 7, 0, 8, 7, 1, 3, 7, 8, 5, 2, 8
OFFSET
0,1
COMMENTS
Icosahedron: A three-dimensional figure with 20 equilateral triangle faces, 12 vertices, and 30 edges.
FORMULA
Sqrt(75 + 30*sqrt(5))/15.
EXAMPLE
0.794654472291766122955530928327594042026590588309264801754955775008438...
MATHEMATICA
R=1; RealDigits[N[(Sqrt[75+30*Sqrt[5]]/15)*R, 175]]
PROG
(PARI) polrootsreal(45*x^4-30*x^2+1)[4] \\ Charles R Greathouse IV, Sep 02 2024
(PARI) sqrt(6/sqrt(5)+3)/3 \\ Charles R Greathouse IV, Sep 02 2024
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
EXTENSIONS
Offset corrected, keyword:cons added by R. J. Mathar, Jul 11 2010
STATUS
approved