A381693 Decimal expansion of the isoperimetric quotient of a truncated icosahedron.

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

Offset

0,1

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for transcendental numbers

Formula

Equals 36*Pi*A377751^2/(A377750^3).

Equals (Pi/12)*(125 + 43*sqrt(5))^2/((10*sqrt(3) + sqrt(5*(5 + 2*sqrt(5))))^3) = A019679*(125 + 43*A002163)^2/((10*A002194 + sqrt(5*(5 + A010476)))^3).

Example

0.90317079253486933111536917369134449479629558352448...

Mathematica

First[RealDigits[Pi/12*(125 + 43*Sqrt[5])^2/(Sqrt[300] + Sqrt[25 + Sqrt[500]])^3, 10, 100]]

Crossrefs

Cf. A377750 (surface area), A377751 (volume).

Cf. A019679, A002163, A002194, A010476, A381684.

Sequence in context: A200306 A153790 A260932 * A062523 A388944 A367961

Adjacent sequences: A381690 A381691 A381692 * A381694 A381695 A381696

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 08 2025

Status

approved