# Viviani curve

The curve of intersection of the surfaces of a sphere of radius $R$ and a certain circular cylinder of radius $R/2$ through the centre of the sphere. The part of the solid sphere located inside the cylinder is known as the Viviani solid. So named after V. Viviani (17th century).

Viviani's window is the set of points in $E^3$ given by $$\{ (x,y,z)\ :\ x^2+y^2+z^2 \le 1\,,\ x^2+y^2 \le x \} \ .$$