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A231984 Decimal expansion of the solid angle (in deg^2) of a spherical square having sides of one degree. 6
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 (list; constant; graph; refs; listen; history; text; internal format)
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...

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 * A100547 A259150 A091668

Adjacent sequences:  A231981 A231982 A231983 * A231985 A231986 A231987

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Nov 17 2013

STATUS

approved

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Last modified May 26 03:13 EDT 2017. Contains 287073 sequences.