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%I #11 Jun 08 2023 08:52:01
%S 3,3,1,6,1,1,9,4,4,8,4,9,6,2,0,0,2,6,9,1,8,6,3,0,2,4,0,1,5,5,8,2,9,7,
%T 3,5,8,0,0,4,7,2,3,2,8,4,1,0,8,7,2,5,8,5,1,3,1,0,0,1,1,8,1,5,5,4,0,3,
%U 7,5,6,5,4,6,4,7,1,8,4,3,4,4,6,6,6,0,7,4,6,0,9,4,9,3,5,1,3,8,7
%N Consider surface area of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the resulting surface area.
%C If you set v[n_] := Pi^(n/2)/(n/2)! and s[n_] := n*Pi^(n/2)/(n/2)! and then Plot[{6.283v[n - 2], s[n]}, {n, 0, 20}], the two curves are almost identical.
%e 33.1611944849620026918630240155829735800472328410872...
%t area[d_] := d * Pi^(d/2)/Gamma[d/2 + 1]; area[x /. FindRoot[PolyGamma[x/2] == Log[Pi], {x, 7}, WorkingPrecision -> 120]] (* _Amiram Eldar_, Jun 08 2023 *)
%Y The dimension is given in A074455.
%Y Cf. A072478, A072479, A074454.
%K cons,nonn
%O 2,1
%A _Robert G. Wilson v_, Aug 22 2002
%E Checked by _Martin Fuller_, Jul 12 2007
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