

A302714


Decimal expansion of 2*sin(Pi/192).


4



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, 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, 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
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OFFSET

1,1


COMMENTS

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. 6974, 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.
This number has been given in Viète's 1595 reply (see A303982 for the link) to Romanus'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


REFERENCES

Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 6974.


LINKS

Table of n, a(n) for n=1..99.
Index entries for sequences related to Chebyshev polynomials.


FORMULA

2*sin(Pi/192) = sqrt(2  sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2 + sqrt(3))))))).


EXAMPLE

2*sin(Pi/192) = 0.03272346325297356328594384696834610047132981567239244974814...


CROSSREFS

Cf. A127672, A302711, A302713, A303982.
Sequence in context: A071189 A137822 A300845 * A193574 A209639 A174238
Adjacent sequences: A302711 A302712 A302713 * A302715 A302716 A302717


KEYWORD

nonn,cons,easy


AUTHOR

Wolfdieter Lang, Apr 28 2018


STATUS

approved



