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

Abstract

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 a^{2} cos^{2} (2k-2)Pi/n+ sin^{2} (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.

Article Title [Persian]

On The Perimeter of an Ellipse

Authors [Persian]

A. Ansari

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

Abstract [Persian]

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 a^{2} cos^{2} (2k-2)Pi/n+ sin^{2} (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.

Keywords [Persian]

Ellipse، Perimeter، Surrounding polygon

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.