A381692 Decimal expansion of the isoperimetric quotient of a truncated dodecahedron.

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

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*A377695^2/(A377694^3).

Equals (Pi/20)*(99 + 47*sqrt(5))^2/((sqrt(3) + 6*sqrt(5 + 2*sqrt(5)))^3) = (A000796/20)*(99 + 47*A002163)^2/((A002194 + 6*sqrt(5 + A010476))^3).

Example

0.7940548943037979813018428272822581808271192993785...

Mathematica

First[RealDigits[Pi/20*(99 + 47*Sqrt[5])^2/(Sqrt[3] + 6*Sqrt[5 + Sqrt[20]])^3, 10, 100]]

Crossrefs

Cf. A377694 (surface area), A377695 (volume).

Cf. A000796, A002163, A002194, A010476, A381684.

Sequence in context: A274169 A121168 A388088 * A102375 A216754 A386742

Adjacent sequences: A381689 A381690 A381691 * A381693 A381694 A381695

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 07 2025

Status

approved