A353407 - OEIS

%I #9 May 07 2022 09:41:17

%S 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,

%T 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,

%U 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

%N 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.

%C The absolute value of the total gravitational attraction force between two identical homogeneous cubes, each with mass M and edge length s, whose centers are at distance s is c*G*M^2/s^2, where G is the gravitational constant (A070058) and c is this constant.

%C The calculation of the closed-form formula for this constant was done by Prof. Bengt Fornberg of the University of Colorado (Trefethen, 2011).

%H Folkmar Bornemann, <a href="https://arxiv.org/abs/2204.02793">The Challenge of Sixfold Integrals: The Closed-Form Evaluation of Newton Potentials between Two Cubes</a>, arXiv:2204.02793 [math.CA], 2022.

%H Jeff Sanny and David M. Smith, <a href="https://doi.org/10.1119/1.4905815">How Spherical Is a Cube (Gravitationally)?</a>, The Physics Teacher, Vol. 53 (2015), pp. 111-113; <a href="https://digitalcommons.lmu.edu/phys_fac/54/">alternative link</a>.

%H Lloyd N. Trefethen, <a href="https://doi.org/10.1007/978-3-642-19533-4_9">Ten digit problems</a>, in: D. Schleicher and M. Lackmann (eds.), An Invitation to Mathematics, Springer, Berlin, Heidelberg, 2011, pp. 119-136; <a href="https://people.maths.ox.ac.uk/~trefethen/publication/PDF/2011_137.pdf">alternative link</a>.

%H Lloyd N. Trefethen, <a href="https://www.lms.ac.uk/sites/lms.ac.uk/files/files/NLMS_491_for%20web.pdf">Two Cubes</a>, LMS Newsletter, Issue 491 (November 2020), p. 17.

%H Michael Trott, <a href="https://blog.wolfram.com/2012/10/23/calculating-the-energy-between-two-cubes/">Calculating the energy between two cubes</a>, News, Views and Insights from Wolfram, Wolfram Blog, October 23, 2012.

%F 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.

%e 0.92598126055729142809343668703833155990642541428277...

%t 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]]

%Y Cf. A070058, A336274, A353769, A353770.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 07 2022