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%I #13 Jun 26 2023 02:21:56
%S 5,2,3,5,3,8,9,6,6,1,5,7,4,6,3,0,5,2,2,1,2,2,3,3,7,1,1,0,8,2,2,5,3,2,
%T 7,5,8,6,7,8,2,0,5,5,3,6,0,2,1,7,2,7,6,4,3,7,5,7,2,6,9,0,1,0,1,6,6,9,
%U 7,8,7,6,7,5,4,2,9,6,5,5,3,5,3,0,9,2,6,0,0,5,0,6,3,3,8,7,5,9,3,2,4
%N Decimal expansion of 2*sin(Pi/120).
%C This constant appears in a historic problem posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593, solved by Viète. See the Havil reference, problem 3, pp. 69-74. See also the comments in A302711 with a link to Romanus book, Exemplum tertium.
%C The solution of the problem uses the special case of an identity R(45, 2*sin(Pi/120)) = 2*sin(3*Pi/8) = A179260 = 1.847759065022..., with a special case of monic Chebyshev polynomials of the first kind, named R, given in A127672.
%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 This constant is 2*sin(Pi/120) = sqrt(2 - sqrt(2 + sqrt(3/16) + sqrt(15/16) + sqrt(5/8 - sqrt(5/64)))) (this is the rewritten x given in the Havil reference on the bottom of page 69).
%e 0.05235389661574630522122337110822532758678205536021727643757...
%t RealDigits[2*Sin[Pi/120], 10, 120][[1]] (* _Amiram Eldar_, Jun 26 2023 *)
%Y Cf. A127672, A179260, A302711.
%K nonn,cons,easy
%O -1,1
%A _Wolfdieter Lang_, Apr 29 2018
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