This model is related to the hyperboloid model as follows. Each point corresponds to a line "L""x" through the origin in R"n"+1, by the definition of projective space. This line intersects the hyperboloid H"n" in a unique point. Conversely, through any point on H"n", there passes a unique line through the origin (which is a point in the projective space). This correspondence defines a bijection between "U""n" and H"n". It is an isometry, since evaluating along reproduces the definition of the distance given for the hyperboloid model.