Look up projective geometry -- homogeneous coordinates are points in 3-d projective space. The defining characteristic of projective points is you can multiply

Look up projective geometry -- homogeneous coordinates are points in 3-d projective space. The defining characteristic of projective points is you can multiply all their coordinates by the same (nonzero) factor without changing the underlying point. (1 0 2 1) equals (2 0 4 2) equals (0.001 0 0.002 0.001). A cool fact about projective space is that every two distinct lines intersect in a point, including parallel lines!