%I #6 Feb 04 2025 15:27:21
%S 2,9,2,3,8,0,4,4,0,0,1,6,3,0,8,7,2,5,2,2,3,2,7,5,4,4,1,3,3,6,6,2,9,1,
%T 7,0,3,8,7,3,5,0,5,6,6,1,5,1,8,9,2,4,4,8,1,7,1,0,6,3,6,9,8,6,3,5,5,3,
%U 4,5,1,6,2,7,9,9,3,5,1,8,0,9,8,3,9,2,5,5,5,8,1,0,3,1,0,2,6,3,1,2,7,1,8,5,4
%N Decimal expansion of cosecant of 20 degrees = csc(Pi/9).
%C 1 + csc(Pi/9) is the radius of the smallest circle into which 11 unit circles can be packed ("r=3.923+ Proved by Melissen in 1994.", according to the Friedman link, which has a diagram). csc(Pi/9) [=1/A019829] is the distance between the center of the larger circle and the center of each unit circle that touches the larger circle.
%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%e 2.9238044001630872522327544133662917...
%t RealDigits[Csc[20 Degree],10,120][[1]] (* _Harvey P. Dale_, May 27 2023 *)
%o (PARI) 1/sin(Pi/9)
%o (PARI) polrootsreal(3*x^6-36*x^4+96*x^2-64)[6] \\ _Charles R Greathouse IV_, Feb 04 2025
%Y Cf. A019829 (1/A121602), A121601.
%K cons,nonn,changed
%O 1,1
%A _Rick L. Shepherd_, Aug 09 2006