The method of mathematical representation in the analysis of planar quadrilateral meshes

The method of the mathematical representation is now numbered among the classical methods of representation. Its contribution is enriching the study of geometric entities and their properties with analysis more accurate and powerful. In this paper we investigate some interesting geometric properties of Planar Quadrilateral mesh (PQ mesh), i.e. polyhedral surfaces defined by symbolic language in researches conducted in recent years by Helmut Pottmann. This particular family of mesh has many applications in computer graphics and contemporary architecture in the delicate transition of discretization of continuous surfaces. With this experience we can put in evidence the significant role of the mathematical representation as bridge with the different sectors of scientific knowledge.