A232814 Decimal expansion of the minimum surface index of a half-open cylinder.

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

Offset

1,1

Comments

Equivalently, the minimum external surface area among all pots or cups (half-open cylinders) delimiting a unit volume. It is attained when the cylinder is right circular and its height matches the radius of its base. We might call it the 'cooking pot constant'. It minimizes the material needed to make the pot (and also its cooling rate). Its determination is a nice exercise in elementary analysis.

For a general definition of surface index, see A232808.

Links

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

Wikipedia, Cylinder (geometry).

Formula

Equals 3*Pi^(1/3) = 3*A092039.

Example

4.3937756626845697890604275817913711752157905668838115230717678...

Mathematica

RealDigits[3 * Surd[Pi, 3], 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)

Crossrefs

Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232815 (closed cones), A232816 (open cones), A232817 (open tubes).

Cf. A092039.

Sequence in context: A276494 A236099 A155536 * A074123 A016704 A131896

Adjacent sequences: A232811 A232812 A232813 * A232815 A232816 A232817

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Dec 04 2013

Status

approved