A374771 - OEIS

%I #13 Jul 20 2024 14:33:50

%S 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,

%T 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,

%U 7,3,1,5,3,0,0,1,0,1,6,8,2,9,8,0,7,2,3,3,6,0

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

%H Paolo Xausa, <a href="/A374771/b374771.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_dodecahedron">Regular dodecahedron</a>.

%F Equals (4/3)*Pi*A237603^3 = 10*A019699*A237603^3.

%F Equals (1/30)*Pi*sqrt(1525 + 682*sqrt(5)).

%F Equals (Pi/6)*A001622^6/((3 - A001622)^(3/2)).

%F Equals A102769*A374772.

%e 5.78333595039657417842182321041033675553722324626...

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

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

%K nonn,cons

%O 1,1

%A _Paolo Xausa_, Jul 19 2024