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Exact Equation of Ellipse Perimeter by Analytical Method

15 July 2022, Version 5
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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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. This is the equation we have been looking for, at least since Leonhard Euler. 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

Aug 16, 2022 Version 8 (Retracted)
Aug 08, 2022 Version 7 (Retracted)
Jul 28, 2022 Version 6 (Retracted)
Jul 15, 2022 Version 5 (Retracted)
Mar 14, 2022 Version 4 (Retracted)
Feb 17, 2022 Version 3 (Retracted)
Feb 15, 2022 Version 2 (Retracted)
Jan 25, 2022 Version 1 (Retracted)

Version Notes

In this version, the DPI of all three figures of the article has been increased.

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

DOI

10.33774/coe-2022-rskdp-v5
D O I: 10.33774/coe-2022-rskdp-v5 [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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