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Some examples of the curve

In mathematics, a Clélie or Clelia curve is a curve parameterized by[1]

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,[2] 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[3] after Clelia Borromeo.[4]