A374771 Decimal expansion of the volume of the sphere inscribed in a regular dodecahedron with unit edge.

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

Author

Paolo Xausa, Jul 19 2024

Keywords

• nonn
• cons

Examples

			5.78333595039657417842182321041033675553722324626...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Regular dodecahedron.

Crossrefs

Cf. A000796, A001622, A019699, A102769, A237603 (radius), A374772.

Programs

Mathematica

First[RealDigits[Pi*Sqrt[1525 + 682*Sqrt[5]]/30, 10, 100]]

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)).

Equals A102769*A374772.