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A243933 Rounded down ratio of a minimum intersection area with a unit circle area in n-symmetrical unit circles intersect in a single point. 1

%I #18 Aug 18 2023 23:51:40

%S 17,5,77,17,210,40,445,77,812,133,1339,210,2056,313,2991,445,4175,610,

%T 5636,812,7403,1054,9506,1339,11973,1672,14835,2056,18120,2494,21856,

%U 2991,26075,3550,30804,4175,36073,4869

%N Rounded down ratio of a minimum intersection area with a unit circle area in n-symmetrical unit circles intersect in a single point.

%C Refer to construction rule in article "Circle-Circle Intersection" in MathWorld.

%C For n > 4, the intersected areas appearing at many sizes. In this case the minimum areas are considered. See illustration in links.

%H Kival Ngaokrajang, <a href="/A243933/a243933.pdf">Illustration of initial terms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Circle-CircleIntersection.html">Circle-Circle Intersection</a>

%F For n > 2, a(n) = floor(Pi/area), where area = 2*arccos(cd/2) - (1/2)*cd*sqrt(4-cd^2), cd = 2*sin(((ang*360/n)*Pi/180)/2), ang = floor((n-1)/2).

%o (PARI) {for (n=3, 100, ang=floor((n-1)/2); cd=2*sin(((ang*360/n)*Pi/180)/2); area=2*acos(cd/2)-(1/2)*cd*(4-cd^2)^(1/2); print1(floor(Pi/area),", "))}

%K nonn

%O 3,1

%A _Kival Ngaokrajang_, Jun 15 2014

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Last modified September 16 14:29 EDT 2024. Contains 375976 sequences. (Running on oeis4.)