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 .