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%I #28 Mar 10 2024 00:24:38
%S 5,9,6,2,0,7,6,5,0,0,8,5,4,7,9,6,8,5,0,6,9,2,1,9,4,5,1,3,5,2,0,1,3,8,
%T 2,1,7,2,6,7,6,7,5,9,9,0,2,0,0,6,7,7,0,3,3,3,1,7,8,7,9,2,1,6,4,6,0,8,
%U 4,3,4,0,4,4,6,3,0,1,1,9,7,2,4,4,4,4,3,0,2,1,6,4,3,7,1,6,2,6,0,4,1,3,4,9,6,5
%N Decimal expansion of 2*sin((37/384)*Pi).
%C This constant is a solution x of R(45, x) = sqrt(2 + sqrt(2 - sqrt(2 - sqrt(2 - sqrt(2 - sqrt(2)))))) = A303982, with the monic Chebyshev polynomial of the first kind, called R, with coefficients given in A127672. This polynomial with the given value appears in the historic problem (exemplum secundum) posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593. However, the two solutions given there (in two different printings) are incorrect. See A303982 for comments and the Vieta link.
%H Adriano Romano Lovaniensi, <a href="https://babel.hathitrust.org/cgi/pt?id=ucm.5320258006;view=1up;seq=14 ">Ideae Mathematicae</a>, 1593.
%H Adriano Romano Lovaniensi, <a href="https://archive.org/stream/bub_gb_qinevzxnHFoC#page/n15/mode/2up">Ideae Mathematicae</a>, 1593 [alternative link with other exemplum 2].
%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(2 + sqrt(3))))))).
%e 0.59620765008547968506921945135201382172676759902006770333178792164608434044...
%t RealDigits[2*Sin[37*Pi/384], 10, 120][[1]] (* _Amiram Eldar_, Jun 26 2023 *)
%o (PARI) 2*sin(37*Pi/384) \\ _Altug Alkan_, May 06 2018
%Y Cf. A127672, A303982.
%K nonn,cons,easy
%O 0,1
%A _Wolfdieter Lang_, May 04 2018
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