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A353770
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Decimal expansion of the gravitational acceleration generated at a vertex 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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4, 1, 9, 7, 5, 7, 3, 3, 9, 8, 8, 7, 1, 0, 6, 2, 9, 1, 8, 7, 3, 7, 4, 7, 6, 8, 7, 2, 0, 0, 8, 1, 3, 9, 0, 9, 6, 0, 5, 8, 5, 6, 1, 0, 2, 7, 6, 1, 7, 7, 2, 6, 6, 1, 3, 8, 7, 8, 2, 7, 5, 6, 1, 7, 1, 2, 7, 6, 5, 7, 4, 5, 1, 0, 4, 7, 7, 6, 7, 5, 7, 6, 6, 1, 4, 8, 8, 7, 0, 3, 0, 2, 5, 9, 9, 8, 8, 7, 0, 6, 4, 5, 9, 7, 1
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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 vertex is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.
The vertices are the positions where the gravitational field that is generated by the cube on its surface attains its minimum 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 (sqrt(3)/2)*(Pi/12 + log(sqrt(2) + 1) - log(sqrt(3) + 2)/2).
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EXAMPLE
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0.41975733988710629187374768720081390960585610276177...
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MATHEMATICA
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RealDigits[(Sqrt[3]/2)*(Pi/12 + Log[Sqrt[2] + 1] - Log[Sqrt[3] + 2]/2), 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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