A121602 Decimal expansion of cosecant of 20 degrees = csc(Pi/9).

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, 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, 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

Offset: 1

Author

Rick L. Shepherd, Aug 09 2006

Keywords

• cons
• nonn

Comments

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.

Examples

			2.9238044001630872522327544133662917...
		

Links

• Index entries for algebraic numbers, degree 6.

Crossrefs

Cf. A019829 (1/A121602), A121601.

Programs

Mathematica

RealDigits[Csc[20 Degree],10,120][[1]] (* Harvey P. Dale, May 27 2023 *)

PARI

1/sin(Pi/9)

PARI

polrootsreal(3*x^6-36*x^4+96*x^2-64)[6] \\ Charles R Greathouse IV, Feb 04 2025