A382012 Decimal expansion of the isoperimetric quotient of a disdyakis triacontahedron.

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

Offset: 0

Author

Paolo Xausa, Mar 20 2025

Keywords

• nonn
• cons
• easy

Comments

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

The disdyakis triacontahedron is the Catalan solid with the highest isoperimetric quotient.

Examples

			0.95776502384780769076187408953240617790783343820517...
		

Links

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

Crossrefs

Cf. A379708 (surface area), A379709 (volume).

Cf. A000796, A381684.

Programs

Mathematica

First[RealDigits[Pi*Root[13997521*#^4 - 1302278*#^2 + 121 &, 4], 10, 100]]

Formula

Equals 36*Pi*A379709^2/(A379708^3).

Equals Pi*r = A000796*r, where r is the largest root of 13997521*x^4 - 1302278*x^2 + 121.