OFFSET
3,1
COMMENTS
The minimum ratio occurs at n = 5.
LINKS
Kival Ngaokrajang, Illustration of initial terms
FORMULA
a(n) = floor(Pi/area(n)) where area = Pi*r(n)^2, r(n) = (s(n)/2)*sqrt((2 - s(n))/(2 + s(n))), with s(n) = 2*sin(Pi/n) which is the side length (length unit 1) of the regular n gon. [rewritten by Wolfdieter Lang, Jun 30 2014 and Jul 02 2014]
a(n) = floor(1/r(n)^2) with r(n) = S(n)*(1 + C(n) - S(n))/(1 + C(n) + S(n)) with S(n) = s(n)/2 and C(n) = cos(Pi/n). 2*C(n) is the ratio of the length of the smallest diagonal and the side length s(n) in the regular n-gon. - Wolfdieter Lang, Jun 30 2014
PROG
(PARI)
{
for (n=3, 100,
c=2*sin(Pi/n);
s=(2+c)/2;
r=sqrt(((s-1)^2*(s-c))/s);
area=Pi*r^2;
a=floor(Pi/area);
print1(a, ", ")
)
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Jun 20 2014
STATUS
approved