%I #16 Mar 27 2021 23:52:53
%S 1,7,9,8,0,7,9,7,4,3,4,1,0,4,7,7,3,4,2,1,5,2,4,5,4,9,5,9,0,4,3,9,6,3,
%T 8,8,2,0,4,2,6,5,9,3,5,0,6,0,0,7,3,9,8,3,9,3,1,0,3,2,3,4,8,7,8,1,2,8,
%U 3,0,6,7,3,4,6,6,7,3,3,5,5,7,3,3,3,9,2
%N Decimal expansion of the surface area of a golden ellipsoid with semi-axes lengths 1, 1 and phi (A001622).
%H Kenneth Brecher, <a href="https://archive.bridgesmathart.org/2015/bridges2015-371.html">The "PhiTOP": A Golden Ellipsoid</a>, Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture, 2015, pp. 371-374.
%H Kenneth Brecher and Rod Cross, <a href="https://doi.org/10.1119/1.5088462">Physics of the PhiTOP</a>, The Physics Teacher, Vol. 57, No. 2 (2019), pp. 74-75.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ellipsoid.html">Ellipsoid</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ellipsoid">Ellipsoid</a>.
%F Equals 2*Pi*(1 + phi*c/sin(c)), where c = arccos(1/phi) (A195692).
%F Equals 2*Pi*(1 + sqrt(2+sqrt(5))*arcsec(phi)).
%e 17.9807974341047734215245495904396388204265935060073...
%t RealDigits[SurfaceArea[Ellipsoid[{0,0,0},{1,1,GoldenRatio}]], 10, 100][[1]]
%t (* requires Mathematica 12+, or *)
%t RealDigits[2*Pi*(1 + GoldenRatio/Sinc[ArcCos[1/GoldenRatio]]), 10, 100][[1]]
%Y Cf. A001622, A195692, A309282.
%K nonn,cons
%O 2,2
%A _Amiram Eldar_, Mar 27 2021