Infinity star, find area?

DraganK

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There are 2n+1 points uniformly distributed on the circumference of the unit circle (radius=1).
If you draw lines that connect every n-th point, you will have a nice looking star.
Find it's area if n -> infinity.
And bonus question:
Find area if there are 2n+2 points?
Scythian, have you found the formula for area?
Say, when we have m points, and any n-th is conected?
 
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