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%I #10 Nov 23 2022 16:18:26
%S 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,
%T 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,
%U 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
%N Decimal expansion of the minimum surface index of an open cone.
%C 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.
%C For a general definition of surface index, see A232808.
%H Stanislav Sykora, <a href="/A232816/b232816.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cone">Cone</a>
%F 3*sqrt(3)*(Pi/6)^(1/3).
%e 4.18807794862313812872559720593668811944052758870434968621283...
%t RealDigits[3 Sqrt[3]Surd[Pi/6,3],10,120][[1]] (* _Harvey P. Dale_, Nov 23 2022 *)
%Y Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232814 (open cylinders), A232815 (closed cones), A232817 (open tubes).
%K nonn,cons,easy
%O 1,1
%A _Stanislav Sykora_, Dec 05 2013
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