Projection of a SphereStereographic projection from a point on a sphere maps the sphere to the plane so that circles on the sphere are projected to circles in the plane, with circles that pass through the point of projection mapping to straight lines in the plane. Here we see colored circular bands on a sphere projected to the plane below; one of the bands (the one containing the point of projection) extends out to infinity. This example is the first step to understanding the projections of the torus that appears in In and Outside the Torus and HopfLink Torus. The movie The Hypersphere: Projections and Foliations, from which this image is taken, describes these ideas more fully. 

