

A238238


Decimal expansion of the polar angle, in radians, of a cone which makes a goldenratio cut of the full solid angle.


4



1, 3, 3, 2, 4, 7, 8, 8, 6, 4, 9, 8, 5, 0, 3, 0, 5, 1, 0, 2, 0, 8, 0, 0, 9, 7, 9, 1, 9, 5, 5, 5, 8, 5, 4, 4, 1, 3, 3, 4, 9, 8, 0, 2, 7, 7, 4, 5, 1, 8, 9, 5, 6, 8, 5, 6, 6, 2, 9, 4, 7, 6, 8, 5, 6, 0, 7, 9, 5, 7, 9, 7, 8, 7, 5, 8, 1, 1, 8, 5, 6, 3, 4, 1, 5, 8, 1
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OFFSET

1,2


COMMENTS

The polar angle (or apex angle) of a cone which cuts a fraction f of the full solid angle (i.e., subtends a solid angle of 4*Pi*f steradians) is given by arccos(12*f). For a golden cut of the sphere surface by a cone with apex in its center, set f = 11/phi, phi being the golden ratio A001622. This value is in radians, its equivalent in degrees is A238239.
The apex angle of the isosceles triangle of smallest perimeter which circumscribes a semicircle (DeTemple, 1992).  Amiram Eldar, Jan 22 2022


LINKS



FORMULA

arccos(12*(11/phi)) = arccos(2/phi1), with phi = A001622.


EXAMPLE

1.3324788649850305102080097919555854413349802774518956856629476856...


MATHEMATICA

RealDigits[ArcCos[2/GoldenRatio 1], 10, 120][[1]] (* Harvey P. Dale, Jul 05 2019 *)


PROG

(PARI) acos(4/(1+sqrt(5))1)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



