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%I #15 May 17 2023 08:41:30
%S 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,
%T 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,
%U 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
%N Decimal expansion of the minimum surface index of a half-open cylinder.
%C 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.
%C For a general definition of surface index, see A232808.
%H Stanislav Sykora, <a href="/A232814/b232814.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cylinder_%28geometry%29">Cylinder (geometry)</a>.
%F Equals 3*Pi^(1/3) = 3*A092039.
%e 4.3937756626845697890604275817913711752157905668838115230717678...
%t RealDigits[3 * Surd[Pi, 3], 10, 120][[1]] (* _Amiram Eldar_, May 17 2023 *)
%Y Cf. Other surface indices: A232808 (spheres), A232809, A232810, A232811, A232812 (platonic solids), A232813 (closed cylinders), A232815 (closed cones), A232816 (open cones), A232817 (open tubes).
%Y Cf. A092039.
%K nonn,cons,easy
%O 1,1
%A _Stanislav Sykora_, Dec 04 2013