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A085365 Decimal expansion of polygon-inscribing 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 (list; constant; graph; refs; listen; history; text; internal format)
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, 1992-12-19 & 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) 120-121.

Kival Ngaokrajang, Illustration of polygon inscribing

R. Stephens, Slowly converging infinite products, Math. Gaz. 79 (486) (1995) 561-565.

Eric Weisstein's World of Mathematics, Polygon Inscribing

Wikipedia, Kepler-Bouwkamp constant

FORMULA

The log of this constant is equal to Sum_{n=1..infinity} ((2^(2n)-1)/n)*zeta(2n)*(zeta(2n)-1-1/2^(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

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Last modified April 21 02:07 EDT 2014. Contains 240824 sequences.