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Some results on the elliptic cycloid. (Alcuni risultati sulla cicloide ellittica.) (Italian)
Archimede 67, No. 2, 59-66 (2015).
Summary: The present work can be placed in the context of classical studies relating to the “roulette”. Consider an ellipse rolling on a straight line; we intend to determine the area subtended by the curve generated by a point located at the endpoint of an axis of the ellipse during a complete rolling. We find a general formula, given by: $A_{\text{CE}}=(2αa^2+b^2)π$, where it is assumed that the point is located at an endpoint of the axis $a$; this result includes the particular case of the area subtended by the ordinary cycloid (the corresponding formula was proved by Torricelli in 1644).
Classification: G70
Keywords: elliptic cycloid