A342571 Decimal expansion of the surface area of a golden ellipsoid with semi-axes lengths 1, 1 and phi (A001622).

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

Offset

2,2

Links

Table of n, a(n) for n=2..88.

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

Cf. A001622, A195692, A309282.

Sequence in context: A010729 A340220 A182688 * A372253 A256924 A377606

Adjacent sequences: A342568 A342569 A342570 * A342572 A342573 A342574

Keyword

nonn,cons

Author

Amiram Eldar, Mar 27 2021

Status

approved