sentences:  To obtain these ones, the hyperbolic plane can be defined as the plane with the following inner product around a point formula_25 with coordinates formula_26
  
  Since the hyperbolic plane is unbounded, the limits of the integral are infinite, and the area can be calculated through
  
  Next it is needed to create a map, which will show that the global information from the hyperbolic plane can be transfer to the surface formula_6, i.e.a global isometry.formula_30 will be the map, whose domain is the hyperbolic plane and image the 2-dimensional manifold formula_6, which carries the inner product from the surface formula_1 with negative curvature.