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%I #5 May 07 2022 09:41:01
%S 9,5,4,8,5,4,6,6,5,9,6,6,1,5,6,7,8,0,1,4,5,5,0,9,5,2,8,0,3,3,6,9,0,5,
%T 8,9,6,0,2,4,7,1,4,7,0,9,8,7,5,7,2,3,4,0,9,8,0,2,0,0,8,3,5,1,3,3,4,2,
%U 7,0,0,4,5,7,9,9,0,5,9,5,5,1,3,2,1,0,3,7,3,5,2,7,7,0,0,1,0,4,7,9,0,6,2,6,2
%N Decimal expansion of the gravitational acceleration generated at a vertex by a unit-mass regular tetrahedron with edge length 2 in units where the gravitational constant is G = 1.
%C The absolute value of the gravitational attraction force between a homogeneous regular tetrahedron with mass M and edge length 2*s and a test particle with mass m located at the tetrahedron's vertex is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.
%C The vertices are the positions where the gravitational field that is generated by the tetrahedron on its surface attains its minimum absolute value.
%H Murray S. Klamkin, <a href="https://www.jstor.org/stable/2132789">Extreme Gravitational Attraction</a>, Problem 92-5, SIAM Review, Vol. 34, No. 1 (1992), pp. 120-121; <a href="https://www.jstor.org/stable/2132502">Solution</a>, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515-520.
%H Eric Weisstein's World of Physics, <a href="https://scienceworld.wolfram.com/physics/PolyhedronGravitationalForce.html">Polyhedron Gravitational Force</a>.
%H Eric Weisstein's World of Physics, <a href="https://scienceworld.wolfram.com/physics/TetrahedronGravitationalForce.html">Tetrahedron Gravitational Force</a>.
%F Equals 6*sqrt(3)*(Pi/3 - arctan(sqrt(2))).
%F Equals 3*sqrt(3)*(Pi/6 - arctan(sqrt(2)/4)).
%e 0.95485466596615678014550952803369058960247147098757...
%t RealDigits[6*Sqrt[3]*(Pi/3 - ArcTan[Sqrt[2]]), 10, 100][[1]]
%Y Cf. A070058, A353769, A353770, A353771, A353773.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, May 07 2022
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