A353407 Decimal expansion of the gravitational force between two unit-edge-length unit-mass cubes whose centers are a unit distance apart, so they are in contact along one face, in units where the gravitational constant is G = 1.
9, 2, 5, 9, 8, 1, 2, 6, 0, 5, 5, 7, 2, 9, 1, 4, 2, 8, 0, 9, 3, 4, 3, 6, 6, 8, 7, 0, 3, 8, 3, 3, 1, 5, 5, 9, 9, 0, 6, 4, 2, 5, 4, 1, 4, 2, 8, 2, 7, 7, 7, 8, 6, 5, 5, 9, 8, 7, 3, 4, 3, 4, 5, 4, 0, 9, 5, 9, 8, 4, 2, 2, 4, 9, 8, 6, 3, 2, 8, 6, 2, 2, 1, 4, 8, 5, 4, 1, 6, 8, 0, 8, 2, 6, 5, 1, 3, 3, 4, 0, 8, 5, 4, 0, 1
Offset: 0
Examples
0.92598126055729142809343668703833155990642541428277...
Links
- Folkmar Bornemann, The Challenge of Sixfold Integrals: The Closed-Form Evaluation of Newton Potentials between Two Cubes, arXiv:2204.02793 [math.CA], 2022.
- Jeff Sanny and David M. Smith, How Spherical Is a Cube (Gravitationally)?, The Physics Teacher, Vol. 53 (2015), pp. 111-113; alternative link.
- Lloyd N. Trefethen, Ten digit problems, in: D. Schleicher and M. Lackmann (eds.), An Invitation to Mathematics, Springer, Berlin, Heidelberg, 2011, pp. 119-136; alternative link.
- Lloyd N. Trefethen, Two Cubes, LMS Newsletter, Issue 491 (November 2020), p. 17.
- Michael Trott, Calculating the energy between two cubes, News, Views and Insights from Wolfram, Wolfram Blog, October 23, 2012.
Programs
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Mathematica
RealDigits[(26*Pi/3 - 14 + 2*Sqrt[2] - 4*Sqrt[3] + 10*Sqrt[5] - 2*Sqrt[6] + 26*Log[2] - 2*Log[5] + 10*Log[Sqrt[2] + 1] + 20*Log[Sqrt[3] + 1] - 35*Log[Sqrt[5] + 1] + 6*Log[Sqrt[6] + 1] - 2*Log[Sqrt[6] + 4] - 22*ArcTan[2*Sqrt[6]])/3, 10, 100][[1]]
Formula
Equals (26*Pi/3 - 14 + 2*sqrt(2) - 4*sqrt(3) + 10*sqrt(5) - 2*sqrt(6) + 26*log(2) - 2*log(5) + 10*log(sqrt(2) + 1) + 20*log(sqrt(3) + 1) - 35*log(sqrt(5) + 1) + 6*log(sqrt(6) + 1) - 2*log(sqrt(6) + 4) - 22*arctan(2*sqrt(6)))/3.
Comments