A second model of the hyperbolic
plane is the upper halfplane
model.
Its points consist in the complex numbers with positive imaginary
parts. The geodesics are the open vertical halflines 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
halfplane 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
in the
upper halfplane works.

