A232816 Decimal expansion of the minimum surface index of an open cone.

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

Offset

1,1

Comments

Equivalently, minimum external surface area among all open cones (not counting the base) enclosing a unit volume. It is attained when the cone is right circular and its height equals the radius of its base multiplied by sqrt(2). We might call it the 'teepee constant', related to the need to minimize the material needed to construct it.

For a general definition of surface index, see A232808.

Links

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

Wikipedia, Cone

Formula

3*sqrt(3)*(Pi/6)^(1/3).

Example

4.18807794862313812872559720593668811944052758870434968621283...

Mathematica

RealDigits[3 Sqrt[3]Surd[Pi/6, 3], 10, 120][[1]] (* Harvey P. Dale, Nov 23 2022 *)

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232815 (closed cones), A232817 (open tubes).

Sequence in context: A116924 A327957 A335707 * A210196 A249252 A128414

Adjacent sequences: A232813 A232814 A232815 * A232817 A232818 A232819

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Dec 05 2013

Status

approved