

A342571


Decimal expansion of the surface area of a golden ellipsoid with semiaxes lengths 1, 1 and phi (A001622).


0



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, 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, 3, 0, 6, 7, 3, 4, 6, 6, 7, 3, 3, 5, 5, 7, 3, 3, 3, 9, 2
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OFFSET

2,2


LINKS

Kenneth Brecher and Rod Cross, Physics of the PhiTOP, The Physics Teacher, Vol. 57, No. 2 (2019), pp. 7475.
Eric Weisstein's World of Mathematics, Ellipsoid.


FORMULA

Equals 2*Pi*(1 + phi*c/sin(c)), where c = arccos(1/phi) (A195692).
Equals 2*Pi*(1 + sqrt(2+sqrt(5))*arcsec(phi)).


EXAMPLE

17.9807974341047734215245495904396388204265935060073...


MATHEMATICA

RealDigits[SurfaceArea[Ellipsoid[{0, 0, 0}, {1, 1, GoldenRatio}]], 10, 100][[1]]
(* requires Mathematica 12+, or *)
RealDigits[2*Pi*(1 + GoldenRatio/Sinc[ArcCos[1/GoldenRatio]]), 10, 100][[1]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



