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

1,2

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

Links

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

Stanislav Sykora, Ad Astra Ltd and Early History of Gravity Engineering

Index entries for algebraic numbers, degree 4

Formula

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

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

Example

1.2408064788027994652549583293109787836682723009035365001...

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A049289 A258053 A099890 * A137511 A011166 A181274

Adjacent sequences: A208742 A208743 A208744 * A208746 A208747 A208748

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Mar 01 2012

Status

approved