A121598 Decimal expansion of cosecant of 180/7 = 25.7142857+ degrees = csc(Pi/7).

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

Offset: 1

Author

Rick L. Shepherd, Aug 09 2006

Keywords

• cons
• nonn
• changed

Comments

1 + csc(Pi/7) is the radius of the smallest circle into which 8 unit circles can be packed ("r=3.304+ Proved by Braaksma in 1963.", according to the Friedman link, which has a diagram).

csc(Pi/7) is the distance between the center of the larger circle and the center of each unit circle that touches the larger circle.

Examples

			2.304764870962486505241150223546855...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• E. Friedman, Erich's Packing Center: "Circles in Circles"
• Index entries for algebraic numbers, degree 6.

Crossrefs

Cf. A121570.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); 1/Sin(Pi(R)/7); // G. C. Greubel, Nov 02 2018

Mathematica

RealDigits[Csc[Pi/7], 10, 100][[1]] (* G. C. Greubel, Nov 02 2018 *)

PARI

1/sin(Pi/7)

Formula

Largest of the 6 real-values roots of 7*x^6 -56*x^4 +112*x^2 -64 =0. - R. J. Mathar, Aug 29 2025