A353772 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.

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, 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, 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

Offset

0,1

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

The vertices are the positions where the gravitational field that is generated by the tetrahedron on its surface attains its minimum absolute value.

Links

Table of n, a(n) for n=0..104.

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 6*sqrt(3)*(Pi/3 - arctan(sqrt(2))).

Equals 3*sqrt(3)*(Pi/6 - arctan(sqrt(2)/4)).

Example

0.95485466596615678014550952803369058960247147098757...

Mathematica

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

Crossrefs

Cf. A070058, A353769, A353770, A353771, A353773.

Sequence in context: A110894 A359282 A198933 * A259148 A089491 A199792

Adjacent sequences: A353769 A353770 A353771 * A353773 A353774 A353775

Keyword

nonn,cons

Author

Amiram Eldar, May 07 2022

Status

approved