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A374771
Decimal expansion of the volume of the sphere inscribed in a regular dodecahedron with unit edge.
4
5, 7, 8, 3, 3, 3, 5, 9, 5, 0, 3, 9, 6, 5, 7, 4, 1, 7, 8, 4, 2, 1, 8, 2, 3, 2, 1, 0, 4, 1, 0, 3, 3, 6, 7, 5, 5, 5, 3, 7, 2, 2, 3, 2, 4, 6, 2, 6, 0, 8, 2, 6, 1, 9, 4, 0, 4, 0, 5, 0, 7, 8, 2, 5, 5, 1, 7, 8, 7, 3, 1, 5, 3, 0, 0, 1, 0, 1, 6, 8, 2, 9, 8, 0, 7, 2, 3, 3, 6, 0
OFFSET
1,1
FORMULA
Equals (4/3)*Pi*A237603^3 = 10*A019699*A237603^3.
Equals (1/30)*Pi*sqrt(1525 + 682*sqrt(5)).
Equals (Pi/6)*A001622^6/((3 - A001622)^(3/2)).
EXAMPLE
5.78333595039657417842182321041033675553722324626...
MATHEMATICA
First[RealDigits[Pi*Sqrt[1525 + 682*Sqrt[5]]/30, 10, 100]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 19 2024
STATUS
approved