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A238238 Decimal expansion of the polar angle, in radians, of a cone which makes a golden-ratio 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 (list; constant; graph; refs; listen; history; text; internal format)
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(1-2*f). For a golden cut of the sphere surface by a cone with apex in its center, set f = 1-1/phi, phi being the golden ratio A001622. This value is in radians, its equivalent in degrees is A238239.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Wikipedia, Solid angle

FORMULA

arccos(1-2*(1-1/phi)) = arccos(2/phi-1), 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

Cf. A001622, A019670, A137914, A238239.

Sequence in context: A161173 A050610 A151848 * A117937 A110897 A116644

Adjacent sequences:  A238235 A238236 A238237 * A238239 A238240 A238241

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Feb 20 2014

STATUS

approved

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Last modified December 8 04:46 EST 2019. Contains 329853 sequences. (Running on oeis4.)