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A231986
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Decimal expansion of the solid angle (in steradians) subtended by a spherical square of one radian side.
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8
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9, 2, 7, 6, 8, 9, 4, 7, 5, 3, 2, 2, 3, 1, 3, 6, 4, 0, 7, 9, 5, 6, 1, 3, 2, 3, 8, 1, 4, 5, 9, 5, 4, 9, 1, 7, 6, 3, 0, 4, 0, 4, 0, 0, 6, 4, 2, 4, 5, 7, 4, 3, 4, 0, 8, 9, 9, 9, 8, 6, 9, 0, 4, 6, 6, 9, 1, 7, 4, 8, 6, 1, 8, 8, 5, 9, 1, 4, 5, 1, 8, 8, 9, 3, 9, 3, 7, 1, 3, 1, 0, 9, 9, 0, 3, 1, 9, 1, 2, 3, 5, 3, 9, 4, 4
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OFFSET
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0,1
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COMMENTS
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In spherical geometry, the solid angle (in steradians) covered by a rectangle with arc-length sides r and s (in radians) equals Omega = 4*arcsin(sin(s/2)*sin(r/2)). For this constant, r = s = 1.
Note: It is a common mistake to think that 1 radian squared gives one steradian! See also the discussion in A231984.
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REFERENCES
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G. V. Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2012, ISBN 978-0691148922.
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LINKS
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FORMULA
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Equals 4*arcsin(sin(1/2)^2).
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EXAMPLE
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0.9276894753223136407956132381459549176304040064245743408999869...
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MATHEMATICA
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RealDigits[4 * ArcSin[Sin[1/2]^2], 10, 120][[1]] (* Amiram Eldar, May 16 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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