|A second model of the hyperbolic
plane is the upper half-plane
Its points consist in the complex numbers with positive imaginary
parts. The geodesics are the open vertical half-lines and semicircles
that are orthogonal to the real axis. As for the conformal disk model,
there is a different metric than in the Euclidean plane, i.e. if we
consider two isometric figures, one close to the boundary of the upper
half-plane and the other a bit further, the one closer to the boundary
will look smaller than the other.
Escher also created a picture that illustrates how the metric
upper half-plane works.