A208745 Decimal expansion of the gravitoid constant.

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

Offset: 1

Author

Stanislav Sykora, Mar 01 2012

Keywords

• nonn
• cons
• easy

Comments

Ratio between the width and the depth of the gravitoid curve delimiting any axial section of a gravidome. A gravidome is an axially symmetric homogeneous body shaped in a way to produce, given a constant mass, the maximum possible gravitation field at a point (the barypole) on its surface. It is shaped like a tomato; with respect to a sphere it is somewhat flattened and the gravitoid constant describes the amount of the flattening. The terms "gravidome" for the body and "gravitoid" for its axial perimeter curve were coined in 2006 by S. Sykora.

A quartic number of denominator 3 with minimal polynomial 27x^4 - 64. - Charles R Greathouse IV, Apr 21 2016

Also the diameter from vertex to opposite vertex of the regular hexagon of unit area. The regular hexagon of unit side has diameter 2 and area (3/2)*sqrt(3) (A104956); scaling that down to unit area yields diameter 2 / sqrt((3/2)*sqrt(3)). - Kevin Ryde, Mar 07 2020

Examples

			1.2408064788027994652549583293109787836682723009035365001...
		

Links

• Stanislav Sykora, Ad Astra Ltd and Early History of Gravity Engineering
• I. J. Zucker, G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Cam. Phil. Soc. 131 (2001) 309 (7.6)
• Index entries for algebraic numbers, degree 4

Programs

Mathematica

RealDigits[2*Sqrt[2/(3*Sqrt[3])],10,120][[1]] (* Harvey P. Dale, Nov 30 2015 *)

PARI

2*sqrt(2/3/sqrt(3)) \\ Charles R Greathouse IV, Aug 25 2015

PARI

polrootsreal(27*x^4-64)[2] \\ Charles R Greathouse IV, Aug 25 2015

Formula

2*sqrt(2/(3*sqrt(3))).

(4/3)^(3/4). - Jon E. Schoenfield, Mar 07 2020

Equals 2F1(1/4,1/2;3/4;3/4) [Zucker] - R. J. Mathar, Jun 24 2024