A231987 - OEIS

A231987

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

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

(list; constant; graph; refs; listen; history; text; internal format)

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

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

EXAMPLE

1.041191803606873340234607533592568788900696676006087134915230281312997...

MATHEMATICA

RealDigits[2*ArcSin[Sqrt[Sin[1/4]]], 10, 120][[1]] (* Amiram Eldar, Jun 06 2023 *)

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), A231896.

Sequence in context: A128137 A232530 A346877 * A376784 A235214 A208606

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

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