

A231987


Decimal expansion of the side length (in radians) of the spherical square whose solid angle is exactly one steradian.


7



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

1,3


COMMENTS

This is an inverse problem (but not an inverse value) to the one leading to A231986: what is the side s of a spherical square (in radians, rad) if it covers a given solid angle (in steradians, sr)? The solution (inverse of the formula in A231896) is s = 2*arcsin(sqrt(sin(Omega/4))). In this particular case, Omega = 1.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
Wikipedia, Solid angle, Section 3.3 (Pyramid)
Wikipedia, Steradian


FORMULA

2*arcsin(sqrt(sin(1/4))).


EXAMPLE

1.041191803606873340234607533592568788900696676006087134915230281312997...


PROG

(PARI)
default(realprecision, 120);
2*asin(sqrt(sin(1/4))) \\ or
solve(x = 1, 2, 4*asin((sin(x/2))^2)  1) \\ least positive solution  Rick L. Shepherd, Jan 28 2014


CROSSREFS

Cf. A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231986 (inverse problem).
Sequence in context: A206438 A128137 A232530 * A235214 A208606 A136100
Adjacent sequences: A231984 A231985 A231986 * A231988 A231989 A231990


KEYWORD

nonn,cons,easy


AUTHOR

Stanislav Sykora, Nov 17 2013


EXTENSIONS

Formula and comment corrected by Rick L. Shepherd, Jan 28 2014


STATUS

approved



