A353771 Decimal expansion of the gravitational acceleration generated at the center of a face by unit-mass regular tetrahedron with edge length 2 in units where the gravitational constant is G = 1.

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

Offset

1,1

Comments

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 center of face is c*G*M*m/s^2, where G is the gravitational constant (A070058) and c is this constant.

The centers of the faces are the positions where the gravitational field that is generated by the tetrahedron attains its maximum absolute value.

Links

Table of n, a(n) for n=1..105.

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.

Eric Weisstein's World of Physics, Polyhedron Gravitational Force.

Eric Weisstein's World of Physics, Tetrahedron Gravitational Force.

Formula

Equals 2*Pi/(3*sqrt(3)) + sqrt(6)*log(sqrt(3) + 2) - 2*sqrt(6)*log(sqrt(3) + sqrt(2))/3.

Example

2.56331181614364946688229395754840795183458511759118...

Mathematica

RealDigits[2*Pi/(3*Sqrt[3]) + Sqrt[6]*Log[Sqrt[3] + 2] - 2*Sqrt[6]*Log[Sqrt[3] + Sqrt[2]]/3, 10, 100][[1]]

Crossrefs

Cf. A070058, A353769, A353770, A353772, A353773.

Sequence in context: A305210 A165501 A274614 * A340859 A336817 A340858

Adjacent sequences: A353768 A353769 A353770 * A353772 A353773 A353774

Keyword

nonn,cons

Author

Amiram Eldar, May 07 2022

Status

approved