|
%I #29 Aug 21 2023 12:16:22
%S 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,
%T 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,
%U 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
%N Decimal expansion of the gravitoid constant.
%C 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.
%C A quartic number of denominator 3 with minimal polynomial 27x^4 - 64. - _Charles R Greathouse IV_, Apr 21 2016
%C 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
%H Stanislav Sykora, <a href="http://dx.doi.org/10.3247/SL1Math06.005">Ad Astra Ltd and Early History of Gravity Engineering</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F 2*sqrt(2/(3*sqrt(3))).
%F (4/3)^(3/4). - _Jon E. Schoenfield_, Mar 07 2020
%e 1.2408064788027994652549583293109787836682723009035365001...
%t RealDigits[2*Sqrt[2/(3*Sqrt[3])],10,120][[1]] (* _Harvey P. Dale_, Nov 30 2015 *)
%o (PARI) 2*sqrt(2/3/sqrt(3)) \\ _Charles R Greathouse IV_, Aug 25 2015
%o (PARI) polrootsreal(27*x^4-64)[2] \\ _Charles R Greathouse IV_, Aug 25 2015
%K nonn,cons,easy
%O 1,2
%A _Stanislav Sykora_, Mar 01 2012
|
