Viviani's curve [SEP] named after
Viviani's curve
In mathematics, particularly geometry, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani, the intersection of a sphere with a cylinder that is tangent to the sphere and passes through the center of the sphere. Before Viviani this curve was studied by Simon de La Loubère and Gilles de Roberval.
The projection of Viviani's curve onto a plane perpendicular to the line through the crossing point and the sphere center is the lemniscate
Clélie
In mathematics, a Clélie or Clelia curve is a curve parameterized by
where "θ" is the longitude and "mθ" is the colatitude.
A curve of this type is confined to the surface of a sphere of radius formula_4, as is obvious from the parametric equations for the surface of a sphere. When formula_5, this is Viviani's curve.
The curve was named by Luigi Guido Grandi after Clelia Borromeo.