

A353772


Decimal expansion of the gravitational acceleration generated at a vertex by a unitmass regular tetrahedron with edge length 2 in units where the gravitational constant is G = 1.


4



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
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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

Murray S. Klamkin, Extreme Gravitational Attraction, Problem 925, SIAM Review, Vol. 34, No. 1 (1992), pp. 120121; Solution, by Carl C. Grosjean, ibid., Vol. 38, No. 3 (1996), pp. 515520.


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



KEYWORD



AUTHOR



STATUS

approved



