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

17, 5, 77, 17, 210, 40, 445, 77, 812, 133, 1339, 210, 2056, 313, 2991, 445, 4175, 610, 5636, 812, 7403, 1054, 9506, 1339, 11973, 1672, 14835, 2056, 18120, 2494, 21856, 2991, 26075, 3550, 30804, 4175, 36073, 4869

Offset

3,1

Comments

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

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

Links

Table of n, a(n) for n=3..40.

Kival Ngaokrajang, Illustration of initial terms

Eric Weisstein's World of Mathematics, Circle-Circle Intersection

Formula

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).

Prog

(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), ", "))}

Crossrefs

Sequence in context: A297982 A298631 A338559 * A145965 A040276 A166211

Adjacent sequences: A243930 A243931 A243932 * A243934 A243935 A243936

Keyword

nonn

Author

Kival Ngaokrajang, Jun 15 2014

Status

approved