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A265729
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Decimal expansion of 32*Pi.
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0
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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
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OFFSET
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3,4
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COMMENTS
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"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)."
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REFERENCES
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The Jun 02 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007)
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LINKS
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FORMULA
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The triple Integral {0-2Pi}, {0-Pi/4}, {0-4} (rho*cos(phi)) rho^2 sin(phi) d(rho) d(phi) d(theta).
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EXAMPLE
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100.53096491487338363080458826494409229430942078000338627119822695385012500...
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MATHEMATICA
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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}]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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