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A353769
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Decimal expansion of the gravitational acceleration generated at the center of a face by a unit-mass cube with edge length 2 in units where the gravitational constant is G = 1.
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5
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6, 4, 9, 2, 2, 4, 1, 4, 4, 5, 6, 4, 5, 9, 1, 2, 6, 4, 7, 1, 2, 4, 7, 4, 7, 4, 2, 4, 4, 6, 6, 8, 2, 0, 3, 1, 5, 3, 5, 9, 5, 0, 1, 6, 4, 6, 9, 1, 0, 4, 1, 9, 3, 1, 3, 4, 8, 7, 8, 0, 0, 3, 3, 4, 0, 3, 3, 2, 2, 1, 2, 8, 6, 1, 7, 1, 1, 1, 5, 9, 9, 4, 3, 1, 3, 1, 4, 4, 2, 9, 8, 3, 8, 6, 5, 2, 6, 4, 0, 8, 2, 9, 9, 0, 0
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OFFSET
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0,1
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COMMENTS
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The absolute value of the gravitational attraction force between a homogeneous cube with mass M and edge length 2*s and a test particle with mass m located at the cube's center of face is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.
The centers of the faces are the positions where the gravitational field that is generated by the cube attains its maximum absolute value.
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LINKS
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Murray S. Klamkin, Extreme Gravitational Attraction, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; Solution, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.
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FORMULA
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Equals Pi/2 + log((sqrt(2) + 1)*(sqrt(6) - 1)/sqrt(5)) - 2*arcsin(sqrt(2/5)).
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EXAMPLE
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0.64922414456459126471247474244668203153595016469104...
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MATHEMATICA
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RealDigits[Pi/2 + Log[(Sqrt[2] + 1)*(Sqrt[6] - 1)/Sqrt[5]] - 2*ArcSin[Sqrt[2/5]], 10, 100][[1]]
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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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