

A302715


Decimal expansion of 2*sin(Pi/120).


3



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, 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, 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
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OFFSET

1,1


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 3, pp. 6974. See also the comments in A302711 with a link to Romanus book, Exemplum tertium.
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.


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

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).


EXAMPLE

2*sin(Pi/120) = 0.05235389661574630522122337110822532758678205536021727643757...


CROSSREFS

Cf. A127672, A179260, A302711.
Sequence in context: A234593 A262429 A097078 * A237200 A021195 A019673
Adjacent sequences: A302712 A302713 A302714 * A302716 A302717 A302718


KEYWORD

nonn,cons,easy


AUTHOR

Wolfdieter Lang, Apr 29 2018


STATUS

approved



