On The Perimeter of an Ellipse

Let E be the ellipse with major and minor radii a and b respectively, and P be its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi- mation for P, it means that we can choose n large enough such that the amount of error be less than any given small number. On the other hand, the formula satises both limit status b→a and b→0 which give respectively P = 2a and P = 4a.