|
%I #32 Jun 26 2023 17:39:53
%S 6,2,3,4,8,9,8,0,1,8,5,8,7,3,3,5,3,0,5,2,5,0,0,4,8,8,4,0,0,4,2,3,9,8,
%T 1,0,6,3,2,2,7,4,7,3,0,8,9,6,4,0,2,1,0,5,3,6,5,5,4,9,4,3,9,0,9,6,8,5,
%U 3,6,5,2,4,5,6,4,8,7,2,8,4,5,7,5,9,4,2,5,0,7,3,2,6,5,8,5
%N Decimal expansion of cos(2*Pi/7) = sin(3*Pi/14) = A255249/2.
%C This number, negated, is a zero of the polynomial 8*x^3 - 4*x^2 - 4*x + 1 that arises in the dissection of a regular heptagon. The other two zeros are cos(Pi/7) (A073052) and sin(Pi/14) (A232736).
%C The old definition was: Decimal expansion of 1/(8*cos(Pi/7)*sin(Pi/14)).
%F Equals 1/(4*cos(Pi/7)-2) = 1/(2*A160389-2). - _Alois P. Heinz_, Jun 25 2023
%F Equals (i^(4/7) - i^(10/7))/2. - _Peter Luschny_, Jun 26 2023
%e 0.6234898018587335305250048840042398106322747308964021053655...
%p Digits := 110: evalf(((-1)^(2/7) - (-1)^(5/7))/2, Digits)*10^96:
%p ListTools:-Reverse(convert(floor(%), base, 10)); # _Peter Luschny_, Jun 25 2023
%t First@ RealDigits[1/(8*Cos[Pi/7]*Sin[Pi/14]), 10, 96] (* _Michael De Vlieger_, Jun 25 2023 *)
%Y Cf. A073052, A160389, A232736, A255249.
%K nonn,cons
%O 0,1
%A _N. J. A. Sloane_, Jun 25 2023
%E Simpler definition from _Alois P. Heinz_, Jun 25 2023.
|
