Area of union of n circles????

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Saptarshi Bhattacharjee 2012-1-4

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https://ww2.mathworks.cn/matlabcentral/answers/25250-area-of-union-of-n-circles

Hello. I am trying to calculate the area of union of n circles in a plane when it is known that all circles are of equal radii and their centers are also known(of all n circles). I was trying to follow the set theory approach where we know the formula for union of n sets. I was just using an operator Ar() which gives the area,i.e. Ar(A) gives me the area of A. I first tried to find out which circle is intersecting with which other circle(s) with the help of D<2R(D=dist between the centers of the two circles), then I was trying to calculate the area of intersection between them pairwise and hence find the area of union. But I am getting stuck for n>4. Can anyone provide a soln to this(soln by the set theory approach is necessary). Thanks in advance