Euler examines families of curves with equal lengths to ellipses, suggesting new mathematical insights.
Euler continues his study of algebraic curves with equal arc length, a subject to which he returned several times. After a brief review, he introduces an infinite family of curves with the same indefinite length as a given ellipse. However, this first family is by his own admission poorly motivated, so he derives directly a different but related family of curves with the same indefinite length as a given ellipse.
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Derek M. Aoki (2026) studied this question.
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