A074456 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.

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, 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, 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

Offset: 2

Author

Robert G. Wilson v, Aug 22 2002

Keywords

• cons
• nonn

Comments

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.

Examples

			33.1611944849620026918630240155829735800472328410872...
		

Crossrefs

The dimension is given in A074455.

Cf. A072478, A072479, A074454.

Programs

Mathematica

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 *)

Extensions

Checked by Martin Fuller, Jul 12 2007