A265729 Decimal expansion of 32*Pi.

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

Offset: 3

Author

Eric W. Weisstein and Robert G. Wilson v, Dec 14 2015

Keywords

• cons
• nonn
• easy

Comments

"The integral corresponds to integration over a spherical cone with opening angle Pi/2 and radius 4. However, it is not clear what the integrand physically represents (it resembles computation of a moment of inertia, but that would give a factor (rho*sin(phi))^2 rather than the given rho*cos(phi))."

Examples

			100.53096491487338363080458826494409229430942078000338627119822695385012500...
		

References

• The Jun 02 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007)

Links

• Eric Weisstein's World of Mathematics, Definite Integral
• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721, A228824, A229939, A061146.

Programs

Mathematica

RealDigits[32 Pi, 10, 111][[1]] (* or *)
Integrate[\[Rho] Cos[\[Phi]] \[Rho]^2 Sin[\[Phi]], {\[Rho], 0, 4}, {\[Phi], 0, Pi/4}, {\[Theta], 0, 2 Pi}]

PARI

32*Pi \\ Altug Alkan, Dec 14 2015

Formula

Equals Integral_{theta=0..2*Pi} Integral_{phi=0..Pi/4} Integral_{rho=0..4} (rho*cos(phi))*rho^2*sin(phi) d(rho) d(phi) d(theta).