The pentagram map and the Boussinesq equation are examples of projectively natural geometric evolution equations. These two examples are "quadrics" and are projectively equivalent. However, any two conic sections are projectively equivalent. A model of the real projective line is the projectively extended real line. The resulting topology is "not" Hausdorff, but may be termed "projectively Hausdorff". A hyperboloid of one sheet is "projectively" equivalent to a hyperbolic paraboloid. "Remark&colon;" A hyperboloid of two sheets is "projectively" equivalent to a sphere. The variety "V" in its projective embedding is projectively normal if "R" is integrally closed. In 8 dimensions there is, projectively, a single pure spinor constraint.