This analysis determines the shape and area of elliptic cycloids traced by rolling ellipses, suggesting insights into their geometric properties.
Given an ellipse rolling along a straight line without slipping and a point P on the ellipse, we will determine the shape of the elliptic cycloid traced by P as the ellipse rolls and compute the area under one arch of the elliptic cycloid. We also investigate the arc length, though we are only able to express it as an integral.
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Pons et al. (2026) studied this question.
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