On The Perimeter of an Ellipse

Abstract

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