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A121601
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Decimal expansion of cosecant of 22.5 degrees = csc(Pi/8).
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5
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also, decimal expansion of 2*sqrt(2)*cos(Pi/8).
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). [From Clark Kimberling, Apr 4 2011]
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REFERENCES
| D. Mumford et al., Indra's Pearls, Cambridge 2002; see p. 362. [From N. J. A. Sloane, Nov 22 2009]
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EXAMPLE
| 2.6131259297527530557132863468543743071675223766985390550977...
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MATHEMATICA
| RealDigits[Csc[Pi/8], 10, 130]
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PROG
| (PARI) 1/sin(Pi/8)
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CROSSREFS
| Cf. A121598.
Sequence in context: A191359 A078434 A021892 * A122761 A100469 A124320
Adjacent sequences: A121598 A121599 A121600 * A121602 A121603 A121604
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KEYWORD
| cons,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 09 2006
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