The term projection has several different, but similar, meanings. A few examples should help clarify the term. First, suppose we are given an object O that is specified as a subset of Euclidean three-dimensional space (E³), and a plane P in E³. The map from O to P that send each point of O to the point in P closest to it, is called the projection map from O to P. For example, suppose that O is a knot - that is a loop of string with its ends glued together. If we spray paint directly at P but in front of the knot O, then the space that is not painted is the projection of O on P. The next example is called polar projection. It is a map f from the unit sphere minus the north pole to the plane z = -1 (this plane is one...