%I #21 Jun 26 2023 06:12:02
%S 3,2,7,2,3,4,6,3,2,5,2,9,7,3,5,6,3,2,8,5,9,4,3,8,4,6,9,6,8,3,4,6,1,0,
%T 0,4,7,1,3,2,9,8,1,5,6,7,2,3,9,2,4,4,9,7,4,8,1,4,1,4,8,7,2,3,7,7,4,6,
%U 6,5,9,6,4,8,0,4,5,1,4,0,5,7,0,8,4,7,4,3,3,4,6,9,8,4,9,7,5,2,7,4,2
%N Decimal expansion of 2*sin(Pi/192).
%C This constant appears in a problem similar to the ones posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593. See the Havil reference, pp. 69-74, problem 2. See the comments on A302713 and A302711, also for the Romanus link. The present identity is R(45, 2*sin(Pi/192)) = 2*sin(15*Pi/64) = A302713, with the monic Chebyshev polynomial R from A127672.
%C This number has been given in Viète's 1595 reply (see A303982 for the link) to Romanus's problems in a corrected Exemplum secundum as solution to the polynomial value given there, which is, in trigonometric version, 2*sin(43*Pi/128) = A303982. Therefore his corrected value (the present one) is also incorrect because it is a solution to the polynomial value 2*sin(15*Pi/64). - _Wolfdieter Lang_, May 04 2018
%D Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 69-74.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.
%F Equals sqrt(2 - sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2 + sqrt(3))))))).
%e 0.03272346325297356328594384696834610047132981567239244974814...
%t RealDigits[2*Sin[Pi/192], 10, 120][[1]] (* _Amiram Eldar_, Jun 26 2023 *)
%Y Cf. A127672, A302711, A302713, A303982.
%K nonn,cons,easy
%O -1,1
%A _Wolfdieter Lang_, Apr 28 2018