OFFSET
1,1
COMMENTS
From Michal Paulovic, May 09 2024: (Start)
This constant multiplied by the square of the side length of a regular enneagon equals the area of that enneagon.
9^2 divided by this constant equals 36 * tan(Pi/9) = 13.10292843... which is the perimeter and the area of an equable enneagon with its side length 4 * tan(Pi/9) = 1.45588093... . (End)
LINKS
FORMULA
Equals (p/4)*cot(Pi/p), with p = 9.
From Michal Paulovic, May 09 2024: (Start)
Equals 9 * sqrt(2 / (1 - sin(5 * A000796 / 18)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(5 * A019669 / 9)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(5 * A019670 / 6)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(5 * A019673 / 3)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(5 * A019676 / 2)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(50 * A019685)) - 1) / 4.
Equals 9 * sqrt(2 / (1 - sin(5 * Pi / 18)) - 1) / 4.
Equals 9 * sqrt(4 / (2 - i^(4/9) - i^(-4/9)) - 1) / 4.
Equals 9 * sqrt(1 / (8 - (-32 + sqrt(-3072))^(1/3) - (-32 - sqrt(-3072))^(1/3)) - 1/16). (End)
EXAMPLE
6.181824193772900127213744059619763614941713348134358098386864...
MAPLE
evalf(9 / (4 * tan(Pi/9)), 100); # Michal Paulovic, May 09 2024
MATHEMATICA
RealDigits[(9/4)*Cot[Pi/9], 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *)
PROG
(PARI) p=9; a=(p/4)*cotan(Pi/p) \\ Use realprecision in excess
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Apr 12 2015
STATUS
approved