A232815 Decimal expansion of the minimum surface index of a closed cone.

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

Offset: 1

Author

Stanislav Sykora, Dec 04 2013

Keywords

• nonn
• cons
• easy

Comments

Equivalently, minimum surface area among all closed cones enclosing a unit volume. It is attained when the cone is right circular and its height equals the diameter of its base multiplied by sqrt(2). Considering one of the ways of marketing ice cream, we might call it the "frozen cone constant".

For a general definition of surface index, see A232808.

Examples

			6.0929477853795556034363160089487569369107615150472...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• Wikipedia, Cone

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232816 (open cones), A232817 (open tubes).

Programs

Mathematica

RealDigits[Surd[72*Pi,3],10,120][[1]] (* Harvey P. Dale, Jul 13 2015 *)

Formula

Equals (72*Pi)^(1/3) = 6*(Pi/3)^(1/3).