|
| |
|
|
A085365
|
|
Decimal expansion of polygon-inscribing constant.
|
|
2
| |
|
|
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; 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 (njas(AT)research.att.com), Feb 10 2008
|
|
|
REFERENCES
| Dick Katz, Problem 91:24, in R. K. Guy, ed., Western Number Theory Problems, 1992-12-19 & 22.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Polygon Inscribing
|
|
|
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 (njas(AT)research.att.com), Feb 10 2008
|
|
|
EXAMPLE
| 0.1149420448532...
|
|
|
CROSSREFS
| Equals 1/A051762.
Sequence in context: A143298 A177839 A013669 * A019767 A021091 A096415
Adjacent sequences: A085362 A085363 A085364 * A085366 A085367 A085368
|
|
|
KEYWORD
| nonn,cons
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jun 25, 2003
|
| |
|
|
