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Analytical Solution for the Perimeter of an Ellipse via a New Definite Integral: A Study on Elliptical Cylinder Sections

16 October 2024, 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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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

Research on the perimeter of an ellipse has so far only found approximations. This occurs because the integral of the perimeter of an ellipse does not have an anti-derivative. Therefore, this study aims to find a new definite integral for the perimeter of an ellipse that has an anti-derivative. This study observed the relationship between the intersection of an elliptical cylinder, which results in a circle, and the perimeter of the base of the elliptical cylinder. This study found a new definite integral to obtain the exact formula for the perimeter of an ellipse, which can be solved analytically.

Keywords

Cylinder section
Lateral Surface
Wave Curve
Transformation
Analytical Solution
Definite Integral
Ellipse Perimeter

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Version History

Oct 16, 2024 Version 2

Version Notes

I made an error in numbering the formulas and writing the length of segment OP, which should be O'P. I also corrected the names x = FF_1 to x-axis = FF_1 and y = DJ_1 to y-axis = DJ_1. I fixed these to avoid any misunderstanding for the readers

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

DOI

10.33774/coe-2024-tn2xn-v2
D O I: 10.33774/coe-2024-tn2xn-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) have declared ethics committee/IRB approval is not relevant to this content

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