A381694 Decimal expansion of the isoperimetric quotient of a (small) rhombicosidodecahedron.

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

Offset: 0

Author

Paolo Xausa, Mar 08 2025

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.93899527411045014134237823698302012883610912007046...
		

Links

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

Crossrefs

Cf. A344149 (surface area), A185093 (volume).

Cf. A000796, A002163, A002194, A381684.

Programs

Mathematica

First[RealDigits[4*Pi*(60 + 29*Sqrt[5])^2/(30 + Sqrt[75] + 3*Sqrt[25 + Sqrt[500]])^3, 10, 100]]

Formula

Equals 36*Pi*A185093^2/(A344149^3).

Equals 4*Pi*(60 + 29*sqrt(5))^2/((30 + 5*sqrt(3) + 3*sqrt(25 + 10*sqrt(5)))^3) = 4*A000796*(60 + 29*A002163)^2/((30 + 5*A002194 + 3*sqrt(25 + 10*A002163))^3).