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A342571 Decimal expansion of the surface area of a golden ellipsoid with semi-axes 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,2
LINKS
Kenneth Brecher, The "PhiTOP": A Golden Ellipsoid, Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture, 2015, pp. 371-374.
Kenneth Brecher and Rod Cross, Physics of the PhiTOP, The Physics Teacher, Vol. 57, No. 2 (2019), pp. 74-75.
Eric Weisstein's World of Mathematics, Ellipsoid.
Wikipedia, 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
Sequence in context: A010729 A340220 A182688 * A372253 A256924 A348668
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 27 2021
STATUS
approved

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Last modified June 17 05:47 EDT 2024. Contains 373432 sequences. (Running on oeis4.)