OFFSET
1,1
COMMENTS
The area of a golden ellipse with a semi-major axis phi and a minor semi-axis 1. - Amiram Eldar, Jul 05 2020
phi*Pi = area of the region having boundaries y = 0, x = Pi/2, and y = (tan x)^(4/5). - Clark Kimberling, Oct 25 2020
LINKS
FORMULA
Equals the nested radical sqrt(Pi^2+sqrt(Pi^4+sqrt(Pi^8+...))). For a proof, see A094885. - Stanislav Sykora, May 24 2016
Equals Integral_{x=0..Pi/2} tan(x)^(4/5) dx. - Clark Kimberling, Nov 18 2020
EXAMPLE
5.0832036923152598158...
MATHEMATICA
First@ RealDigits[N[GoldenRatio Pi, 120]] (* Michael De Vlieger, May 24 2016 *)
PROG
(PARI) { default(realprecision, 20080); phi=(1+sqrt(5))/2; x=phi*Pi; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b094886.txt", n, " ", d)); } \\ Harry J. Smith, Apr 27 2009
(PARI) Pi*(1+sqrt(5))/2 \\ Michel Marcus, May 25 2016
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
N. J. A. Sloane, Jun 15 2004
STATUS
approved