

A085365


Decimal expansion of polygoninscribing constant.


3



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

0,3


COMMENTS

Inscribe an equilateral triangle in a circle of unit radius. Inscribe a circle in the triangle. Inscribe a square in the second circle and inscribe a circle in the square. Inscribe a regular pentagon in the third circle and so on. The radii of the circles converge to Product_{ k = 3..infinity } cos(Pi/k), which is this number.  N. J. A. Sloane, Feb 10 2008


REFERENCES

Dick Katz, Problem 91:24, in R. K. Guy, ed., Western Number Theory Problems, 19921219 & 22.


LINKS

Table of n, a(n) for n=0..101.
M. Chamberland, A. Straub, On Gamma quotients and infinite products, arXiv:1309.3455, Section 4.
Clive J. Grimstone, A product of cosines, Math. Gaz. 64 (428) (1980) 120121.
Kival Ngaokrajang, Illustration of polygon inscribing
R. Stephens, Slowly converging infinite products, Math. Gaz. 79 (486) (1995) 561565.
Eric Weisstein's World of Mathematics, Polygon Inscribing
Wikipedia, KeplerBouwkamp constant


FORMULA

The log of this constant is equal to Sum_{n=1..infinity} ((2^(2n)1)/n)*zeta(2n)*(zeta(2n)11/2^(2n)). [Richard McIntosh]  N. J. A. Sloane, Feb 10 2008


EXAMPLE

0.1149420448532...


CROSSREFS

Equals 1/A051762.
Cf. A131671.
Sequence in context: A143298 A177839 A013669 * A019767 A021091 A096415
Adjacent sequences: A085362 A085363 A085364 * A085366 A085367 A085368


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Jun 25 2003


STATUS

approved



