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A302716 Decimal expansion of 2*sin(Pi/675). 3


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

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

%U 6,6,4,7,6,2,7,3,4,3,2,2,2,7,2,4,3,1,5,9,0,5,7,5,1,5,4,1,1,5,5,7

%N Decimal expansion of 2*sin(Pi/675).

%C This constant appears in a historic problem posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593, solved by Vi├Ęte. See the Havil reference, problem 4, pp. 69-74. See also the comments, references and links in A302711.

%C The present identity is R(45, 2*sin(Pi/675)) = 2*sin(Pi/15) = A272534 = 0.415823381635518..., 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/675).

%e 0.0093083890713223248278454073630973484911817874590184488122045378391206664762...

%t RealDigits[2 Sin[Pi/675], 10, 111][[1]] (* _Robert G. Wilson v_, Apr 29 2018 *)

%o (PARI) 2*sin(Pi/675) \\ _Altug Alkan_, May 01 2018

%Y Cf. A127672, A272534, A302711.

%K nonn,cons,easy

%O -2,1

%A _Wolfdieter Lang_, Apr 29 2018

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Last modified July 18 11:30 EDT 2019. Contains 325138 sequences. (Running on oeis4.)