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Explores a new elliptic perimeter formula, suggesting better approximation methods.
This paper presents an alternative derivation of the perimeter formula of an ellipse by combining projection and calculus. It offers a different perspective compared to traditional integration methods. The purpose of this paper is to illustrate the geometrical properties of ellipses. In addition, it further develops the projection method to obtain a summation approximation based on projection, with an O(x⁻⁴) convergence rate and a relative error mostly independent of the eccentricity when e is not near $1$, which is proved rigorously via asymptotic error analysis.
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Jialun Yang (2024) studied this question.
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