On The Perimeter of an Ellipse
محورهای موضوعی : Applied Mathematics
1 - Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.
کلید واژه: Ellipse, Perimeter, Surrounding polygon,
چکیده مقاله :
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.
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) 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 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.
[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.
