A353773 - OEIS

%I #5 May 07 2022 09:40:56

%S 6,4,7,0,5,8,8,2,7,5,9,7,8,4,7,3,5,8,2,3,7,9,0,6,1,9,4,7,4,6,1,7,4,6,

%T 6,8,5,4,7,7,4,2,9,8,0,4,6,7,8,6,6,8,1,4,6,7,8,0,1,1,8,3,1,5,5,4,1,6,

%U 2,6,2,7,5,5,0,0,0,9,4,1,3,7,3,1,6,0,7,7,7,9,2,6,2,3,0,1,8,8,4,7,6,7,8,3,1

%N Decimal expansion of the gravitational acceleration generated at a vertex by a unit-mass regular octahedron 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 octahedron with mass M and edge length 2*s and a test particle with mass m located at the octahedron'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 octahedron 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/OctahedronGravitationalForce.html">Octahedron Gravitational Force</a>.

%H Eric Weisstein's World of Physics, <a href="https://scienceworld.wolfram.com/physics/PolyhedronGravitationalForce.html">Polyhedron Gravitational Force</a>.

%F Equals sqrt(2)*log(3*(sqrt(2)-1)) + arctan(sqrt(2)/4).

%e 0.64705882759784735823790619474617466854774298046786...

%t RealDigits[Sqrt[2]*Log[3*(Sqrt[2]-1)] + ArcTan[Sqrt[2]/4], 10, 100][[1]]

%Y Cf. A070058, A353769, A353770, A353771, A353772.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 07 2022