A302716 - OEIS

A302716

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

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, 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, 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

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OFFSET

-2,1

COMMENTS

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 4, pp. 69-74. See also the comments, references and links in A302711.

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.

REFERENCES

Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 69-74.

LINKS

Table of n, a(n) for n=-2..97.

Index entries for sequences related to Chebyshev polynomials.

FORMULA

This constant is 2*sin(Pi/675).

EXAMPLE

0.0093083890713223248278454073630973484911817874590184488122045378391206664762...

MATHEMATICA

RealDigits[2 Sin[Pi/675], 10, 111][[1]] (* Robert G. Wilson v, Apr 29 2018 *)

PROG