I don't need the full solution, just give me some hints as much as posible, and can someone tell me how this question is related to conservative vector field? in the following part, j is always a subscript, sum(wj,j=1..n) means to calculate the sum of wj from j=1 to j=n, I hope this writing style can be understood cos no way to type the math notation here.
Consider a closed polygon with vertices,v1,v2,...,vn,vn+1=v1, arranged in the positive direction and let v be a point inside the polygon. Show that
v=(sum(wjvj,j=1..n)/(sum(wj,j=1..n))
where wj=tan( (alpha(j-1))/2 + tan(alpha(j)/2) / modulusof(vj-v),j=1,2,...n and alpha(j) is the angle with |alpha(j)|
2007-11-05
01:30:37
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3 answers
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Mathematics