On The Perimeter of an Ellipse

Subject Areas : Applied Mathematics

A.  Ansari ¹ (Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.)

Received: 2015-09-30 Accepted : 2015-09-30 Published : 2012-12-01

Keywords: Ellipse, Perimeter, Surrounding polygon,

Abstract :

Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2)Σa2 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 amountof error be less than any given small number. On the other hand, the formulasatises both limit status b→a and b→0 which give respectively P = 2a andP = 4a.

References:

[1] Gerard P. Michon, www.numericana.com/answer/ellipse.htm
[2] Gerald B. Folland, Real Analysis, Modern Techniques And Their Applications,
John Wiley And Sons, Second Edition.
[3] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, Third Edition
[4] George B. Thomas, Ross L. Finney Calculus And Analytic Geometry, Addison-
Wesley, Ninth Edition.