On The Perimeter of an Ellipse

Theory of Approximation and Applications

مقاله 1، دوره 6، شماره 2، اسفند 2012، صفحه 1-6   

نوع مقاله: Research Articles

نویسنده

A. Ansari^*

Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.

چکیده

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
satises both limit status b→a and b→0 which give respectively P = 2a and
P = 4a.

مراجع

[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.