A302712 - OEIS

A302712

Decimal expansion of 2*sin(Pi/96).

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

(list; constant; graph; refs; listen; history; text; internal format)

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 1 (with a correction), pp. 69-74.

For details see the comments under A302711, also for the original reference.

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=-1..100.

FORMULA

The constant is 2*sin(Pi/96) = sqrt(2 - sqrt(2 + sqrt(2 + sqrt(2 + sqrt(3))))).

EXAMPLE

2*sin(Pi/96) = 0.0654381656435522841273198526345762522299252545033923937561...

MATHEMATICA

RealDigits[2*Sin[Pi/96], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

CROSSREFS