Study illustrates geometrical properties of ellipses through projection and calculus, suggesting a new method.
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 almost independent of the eccentricity.
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Jialun Yang (2026) studied this question.
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