In mathematics, particularly geometry, **Viviani’s curve**, also known as **Viviani’s window**, is a figure eight shaped space curve named after the Italian mathematicianVincenzo Viviani, the intersection of a sphere with a cylinder that is tangent to the sphere and passes through the center of the sphere.

The projection of Viviani’s curve onto a plane perpendicular to the line through the crossing point and the sphere center is the lemniscate of Gerono.

The curve can be obtained by intersecting a sphere of radius centered at the origin,

with the cylinder centered at of radius given by

The resulting curve of intersection, , can be parameterized by to give the parametric equation of Viviani’s curve:

This is a clelie with , where .