id: 06644791
dt: j
an: 2016f.01057
au: Franco, Francesco
ti: Some results on the elliptic cycloid. (Alcuni risultati sulla cicloide
ellittica.)
so: Archimede 67, No. 2, 59-66 (2015).
py: 2015
pu: Le Monnier, Firenze
la: IT
cc: G70
ut: elliptic cycloid
ci:
li:
ab: 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).
rv: