Definition of a Tangent Plane We all have and intuitive idea of what the tangent plane to a point on a given surface should be. It is the plane that goes through that point and that it is tangent to the surface at that point. Suppose. z = f(x,y) is a smooth surface above the xy-plane (see the picture below).
The two prokaryotic domains (or empires),  Bacteria  (or  Eubacteria ) and  Archaea  (or  Archaeobacteria ), are subdivided into 35 phyla (or divisions): 30 phyla in the domain  Bacteria , and 5 phyla in the domain  Archaea .
Phylogenies based on small subunit r RNA, however, show that the eubacteria are marked by 10 or 11 deep clades that we interpret as kingdoms (see Figure 1). This could just be the tip of the iceberg with respect to their true diversity. Garrity et al.