cp's OEIS Frontend

A244093 Rounded down ratio of area of a unit circle and a circle inscribed in any of the n triangles composing a regular n-gon which is circumscribed by a unit circle.

%I A244093 #22 Sep 16 2019 12:40:28
%S A244093 18,11,11,12,13,15,17,19,22,25,28,31,35,39,42,47,51,56,60,65,70,76,81,
%T A244093 87,93,99,106,112,119,126,133,141,148,156,164,173,181,190,198,207,217,
%U A244093 226,236,246,256,266,276,287,298,309,320,332,343,355,367,380,392,405,418,431,444
%N A244093 Rounded down ratio of area of a unit circle and a circle inscribed in any of the n triangles composing a regular n-gon which is circumscribed by a unit circle.
%C A244093 The minimum ratio occurs at n = 5.
%H A244093 Kival Ngaokrajang, <a href="/A244093/a244093_2.pdf">Illustration of initial terms</a>
%F A244093 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]
%F A244093 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
%o A244093 (PARI)
%o A244093 {
%o A244093   for (n=3, 100,
%o A244093      c=2*sin(Pi/n);
%o A244093      s=(2+c)/2;
%o A244093      r=sqrt(((s-1)^2*(s-c))/s);
%o A244093      area=Pi*r^2;
%o A244093      a=floor(Pi/area);
%o A244093      print1(a,", ")
%o A244093   )
%o A244093 }
%Y A244093 Cf. A244094, A244096.
%K A244093 nonn
%O A244093 3,1
%A A244093 _Kival Ngaokrajang_, Jun 20 2014