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A121601 Decimal expansion of cosecant of 22.5 degrees = csc(Pi/8). 6
2, 6, 1, 3, 1, 2, 5, 9, 2, 9, 7, 5, 2, 7, 5, 3, 0, 5, 5, 7, 1, 3, 2, 8, 6, 3, 4, 6, 8, 5, 4, 3, 7, 4, 3, 0, 7, 1, 6, 7, 5, 2, 2, 3, 7, 6, 6, 9, 8, 5, 3, 9, 0, 5, 5, 0, 9, 7, 7, 9, 6, 7, 3, 3, 8, 1, 6, 1, 6, 2, 0, 8, 2, 9, 2, 2, 3, 8, 4, 1, 0, 1, 9, 0, 3, 7, 0, 7, 4, 4, 0, 3, 8, 5, 2, 5, 6, 2, 8, 6, 4, 9, 2, 7, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

1 + csc(Pi/8) is the radius of the smallest circle into which 9 unit circles can be packed ("r=3.613+ Proved by Pirl in 1969", according to the Friedman link, which has a diagram).

csc(Pi/8) is the distance between the center of the larger circle and the center of each unit circle that touches the larger circle.

A rectangle of length L and width W is a called a silver rectangle if L=rW, where r is the silver ratio; i.e., r = 1+sqrt(2). The diagonal has length D = sqrt(W^2+L^2), so that D/W = sqrt(4+2*sqrt(2)) = csc(Pi/8). - Clark Kimberling, Apr 04 2011

REFERENCES

D. Mumford et al., Indra's Pearls, Cambridge 2002; see p. 362. [From N. J. A. Sloane, Nov 22 2009]

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Equals 2*sqrt(2)*cos(Pi/8).

EXAMPLE

2.6131259297527530557132863468543743071675223766985390550977...

MAPLE

evalf(1/sin(Pi/8), 120); # Muniru A Asiru, Nov 02 2018

MATHEMATICA

RealDigits[Csc[Pi/8], 10, 130][[1]] (* corrected by Harvey P. Dale, Jul 28 2012 *)

PROG

(PARI) 1/sin(Pi/8)

(MAGMA) SetDefaultRealField(RealField(100)); R:=RealField(); 1/Sin(Pi(R)/8); // G. C. Greubel, Nov 02 2018

CROSSREFS

Cf. A121598.

Sequence in context: A021892 A269224 A257240 * A122761 A100469 A124320

Adjacent sequences:  A121598 A121599 A121600 * A121602 A121603 A121604

KEYWORD

cons,nonn

AUTHOR

Rick L. Shepherd, Aug 09 2006

STATUS

approved

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Last modified July 22 17:02 EDT 2019. Contains 325225 sequences. (Running on oeis4.)