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Decimal expansion of the conversion factor from radians to arcseconds.
10

%I #67 Jun 05 2024 12:08:22

%S 2,0,6,2,6,4,8,0,6,2,4,7,0,9,6,3,5,5,1,5,6,4,7,3,3,5,7,3,3,0,7,7,8,6,

%T 1,3,1,9,6,6,5,9,7,0,0,8,7,9,6,3,1,5,5,7,5,7,6,9,7,6,8,7,7,9,0,0,3,3,

%U 0,2,4,9,7,3,3

%N Decimal expansion of the conversion factor from radians to arcseconds.

%C From _Peter Munn_, Aug 21 2020 and Nov 11 2020: (Start)

%C Corresponds to a significant mark labeled with a (typographic) double prime symbol on slide rule calculating devices in the 20th century. The Pickworth reference explains its use for sines and tangents of small angles.

%C As tangents of small angles can be approximated by the angle itself, this value approximates the cotangent of an arcsecond, and so, to within 1 part in 10^11, the number of astronomical units in a parsec, prior to its redefinition in August 2015. (End)

%C Equals the number of astronomical units in a parsec, as defined in 2015. - _Donghwi Park_, Aug 08 2021

%D C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London, 1945, pp. 76-78, Trigonometrical Applications.

%H Robert G. Wilson v, <a href="/A217572/b217572.txt">Table of n, a(n) for n = 6..1005</a>

%H Peter Munn, <a href="/A337092/a337092.jpg">Aristo 89 Slide Rule</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Parsec">Parsec</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Minute_and_second_of_arc">Minute and second of arc</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals 3600 * A072097.

%F Equals 1/A155970.

%e 206264.806247096355156473...

%p evalf(180/Pi*3600) ;

%t RealDigits[(180/Pi) 3600, 10, 75][[1]] (* _Bruno Berselli_, Oct 10 2012 *)

%o (Maxima) fpprec:77; ev(bfloat((180/%pi)*3600)); // _Bruno Berselli_, Oct 10 2012

%Y Related conversion factors: A155970 (arcseconds to radians), A072097 (radians to degrees), A337493 (radians to arcminutes).

%K cons,nonn,easy

%O 6,1

%A _R. J. Mathar_, Oct 10 2012