A381691 Decimal expansion of the isoperimetric quotient of an icosidodecahedron.

8, 6, 0, 1, 5, 1, 2, 9, 1, 9, 2, 9, 0, 0, 5, 7, 3, 6, 9, 3, 4, 9, 8, 8, 7, 1, 7, 5, 5, 1, 1, 0, 4, 8, 0, 7, 6, 6, 8, 1, 6, 4, 2, 5, 3, 4, 6, 3, 9, 7, 9, 6, 5, 5, 6, 9, 0, 2, 5, 9, 7, 6, 2, 8, 7, 5, 7, 5, 0, 9, 1, 7, 9, 5, 8, 3, 2, 0, 3, 3, 6, 1, 1, 4, 0, 3, 1, 3, 6, 0

Offset: 0

Author

Paolo Xausa, Mar 07 2025

Keywords

• nonn
• cons
• easy

Comments

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

Examples

			0.86015129192900573693498871755110480766816425346...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers

Crossrefs

Cf. A179451 (surface area), A179450 (volume).

Cf. A000796, A002163, A010464, A381684.

Programs

Mathematica

First[RealDigits[Pi*(765 + 347*#)/(15*Sqrt[6]*(10 + 3*# + Sqrt[75 + 30*#])^(3/2)) & [Sqrt[5]], 10, 100]]

Formula

Equals 36*Pi*A179450^2/(A179451^3).

Equals Pi*(765 + 347*sqrt(5))/(15*sqrt(6)*(10 + 3*sqrt(5) + sqrt(75 + 30*sqrt(5)))^(3/2)) = A000796*(765 + 347*A002163)/(15*A010464*(10 + 3*A002163 + sqrt(75 + 30*A002163))^(3/2)).