A231984 Decimal expansion of the solid angle (in deg^2) of a spherical square having sides of one degree.

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

Offset

0,1

Comments

See the comments to A231983 which will make it clear why on a sphere the solid angle of a square with one degree arc-length side is not exactly one deg^2. The correct value, shown here, is A231983*A231981.

References

G. V. Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2012, ISBN 978-0691148922.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Solid angle, Section 3.3 (Pyramid)

Wikipedia, Square degree

Wikipedia, Steradian

Formula

4*arcsin(sin(R/2)sin(S/2))*(180/Pi)^2, where R = S = Pi/180.

Example

0.9999746164392786543219850947849682255179591524185764527406467...

Mathematica

RealDigits[4*ArcSin[Sin[Pi/360]^2](180/Pi)^2, 10, 120][[1]] (* Harvey P. Dale, Aug 20 2017 *)

Prog

(PARI)
default(realprecision, 120);
4*asin(sin(Pi/360)^2)*(180/Pi)^2 \\ Rick L. Shepherd, Jan 28 2014

Crossrefs

Cf. A000796 (Pi), A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231983 (this constant in sr), A231987 (for square with 1 rad side), A231985, A231986.

Sequence in context: A111691 A093409 A111692 * A346436 A346583 A346570

Adjacent sequences: A231981 A231982 A231983 * A231985 A231986 A231987

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Nov 17 2013

Status

approved