

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
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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



