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A243933
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Rounded down ratio of a minimum intersection area with a unit circle area in n-symmetrical unit circles intersect in a single point.
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1
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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
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OFFSET
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3,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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).
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PROG
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(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), ", "))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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