Mathematical Experiment 5

Construct the spiral as thus:

The stereographic projection from the xy plane to the unit sphere is given by f(x,y) =

Select a circle C orthogonal to the unit circle in the xy plane. Construct the surface formed by the line segments connecting points on C to the corresponding stereographic images.

Construct three cylinders with any two touching at one point.

Construct one-half of the tangent cone to a sphere.

Construct one-half of a right solid cylinder whose boundary consists of the helicoid, part of the cylinder and two semi-disks.

Construct the cyclide by inverting a torus.