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arXiv · 2509.13173

Euler's explorations of extremal ellipses

Leonhard Euler·Jonathan David Evans
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Abstract

In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from the original Latin, together with a commentary which discusses Euler's results and an appendix which addresses a question from E691 which Euler left for others to consider.

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Leonhard Euler, Jonathan David Evans. 2025-09-16. Euler's explorations of extremal ellipses. https://arxiv.org/abs/2509.13173

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