
06644791
j
2016f.01057
Franco, Francesco
Some results on the elliptic cycloid. (Alcuni risultati sulla cicloide ellittica.)
Archimede 67, No. 2, 5966 (2015).
2015
Le Monnier, Firenze
IT
G70
elliptic cycloid
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: $A_{\text{CE}}=(2\alpha a^2+b^2)\pi$, 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).