A231986 Decimal expansion of the solid angle (in steradians) subtended by a spherical square of one radian side.

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

Offset

0,1

Comments

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.

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, Steradian.

Formula

Equals 4*arcsin(sin(1/2)^2).

Example

0.9276894753223136407956132381459549176304040064245743408999869...

Mathematica

RealDigits[4 * ArcSin[Sin[1/2]^2], 10, 120][[1]] (* Amiram Eldar, May 16 2023 *)

Crossrefs

Cf. A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231984, A231987 (inverse problem).

Sequence in context: A172423 A104696 A086088 * A347329 A203126 A111506

Adjacent sequences: A231983 A231984 A231985 * A231987 A231988 A231989

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Nov 17 2013

Status

approved