Resumen de Proyecciones estereográficas y Geométricas en el plano
The classic construction by Cayley and Klein, that associates the Euclidean plane with the R_algebra C or by stereographic projection with the quadric of points (Sphere), allow us to represent the inversive group as a matrix group In a sequence of three papers, that begins with this one, we are going to translate this classic construction, to the three types of metrics in the plane: euclidean, hyperbolic and degenerate. To do this we only have to change the R_algebra and the quadric that we associate to the metric plane.
This first paper, is devoted to the study of stereographic projection, which is the basic tool that connects the three geometrical objects: metric plane, R_algebra and quadric.
