Clélie

File:Clelies curve.png

Some examples of the curve

In mathematics, a Clélie or Clelia curve is a curve parameterized by

$x=a \sin(m\theta) \cos(\theta)$

$y=a \sin(m\theta) \sin(\theta)$

$z=a \cos(m\theta)$

A curve of this type is confined to the surface of a sphere of radius $a$, as is obvious from the parametric equations for the surface of a sphere. When $m=1$, this is Viviani's curve.

The curve was named by Luigi Guido Grandi after Clelia Borromeo.