A Refined Symmetric Mean Integral Approach to Bounding the Perimeter of an Ellipse

harun abdul rohman

doi:10.33774/coe-2025-5bb4j

Mathematics

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A Refined Symmetric Mean Integral Approach to Bounding the Perimeter of an Ellipse

22 April 2025, Version 1

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harun abdul rohman

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Abstract

We refine the symmetric mean integral method for estimating the perimeter of an ellipse by restricting the integration limits to [0, π/4]. This approach allows the application of the squeeze theorem by leveraging the extremal behavior of the integrand, yielding explicit upper and lower bounds. The results provide a foundation for further research to derive improved perimeter estimates for ellipses.

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