A381671 Decimal expansion of the isoperimetric quotient of a regular tetrahedron.

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

Offset

0,1

Comments

Polya (1954) defines the isoperimetric quotient of a solid as 36*Pi*V^2/(S^3), where V and S are the volume and surface area of the solid, respectively.

The isoperimetric quotient of a sphere is 1.

References

George Polya, Mathematics and Plausible Reasoning, Vol. 1: Induction and Analogy in Mathematics, Princeton University Press, Princeton, New Jersey, 1954. See pp. 188-189, exercise 43.

Links

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

Formula

Equals Pi/(6*sqrt(3)) = A019673/A002194.

Example

0.30229989403903630843234637627369262204734437468212...

Mathematica

First[RealDigits[Pi/(6*Sqrt[3]), 10, 100]]

Crossrefs

Cf. A273633 (sphericity).

Cf. isoperimetric quotient of other Platonic solids: A019673 (cube), A073010 (octahedron), A374772 (dodecahedron), A381672 (icosahedron).

Cf. A002194, A019673.

Sequence in context: A371981 A280238 A154574 * A119493 A355344 A224317

Adjacent sequences: A381668 A381669 A381670 * A381672 A381673 A381674

Keyword

nonn,cons,easy

Author

Paolo Xausa, Mar 03 2025

Status

approved