We discuss a new covariant approach to geometry, called conformal geometric algebra, concentrating particularly on applications to projective geometry and new hybrid geometries. In addition, a new method of working, which can achieve similar results, but using only one extra dimension instead of two, is also discussed.

Anthony Lasenby, **Recent Applications of Conformal Geometric Algebra, **H. Li, P. J. Olver and G. Sommer (Eds.): IWMM 2004, LNCS 3519 Springer-Verlag (2005)