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Exact Equation of Ellipse Perimeter by Analytical Method

15 February 2022, Version 2
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

As you know, we do not have any exact equation for calculating the perimeter of an ellipse. In this article, we obtain this equation analytically. In this article we will find a way for derivation of the solution of Elliptic integral in terms of elementary functions.

Keywords

Ellipse perimeter
Ellipse
Perimeter
Elliptic integral

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Version History

Feb 15, 2022 Version 2

Version Notes

In mathematics and physics articles, because the author's mind is involved in a lot of calculations and analysis, despite a lot of effort, accuracy and editing, fundamental errors can still occur, and the advantage of preprint is that these errors can be solve quickly. In the Jan 25 2022 version, I also made a big mistake and assumed for the ellipse √(1-ϵ^2 )<1-ϵ^2 (ϵ is eccentricity of ellipse), which we know this point is wrong and we have: √(1-ϵ^2 )>1-ϵ^2 . This mistake changed my thoughts and put the whole article in the wrong direction. In the new version of the article, the idea is the same as the previous one, namely extraction the perimeter of ellipse using its associated circle.

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2022-rskdp-v2
D O I: 10.33774/coe-2022-rskdp-v2 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) declare that they have sought and gained approval from the relevant ethics committee/IRB for this research and its publication.

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