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

Author

Paolo Xausa, Mar 03 2025

Keywords

• nonn
• cons
• easy

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.

Examples

			0.30229989403903630843234637627369262204734437468212...
		

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

Crossrefs

Cf. A273633 (sphericity).

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

Cf. A002194, A019673.

Programs

Mathematica

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

Formula

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