12: Hyperbolic Lane
In this chapter, we use inversive geometry to construct the model of a hyperbolic plane — a neutral plane that is not Euclidean. Namely, we construct the so-called conformal disc model of the hyperbolic plane. This model was discovered by Beltrami in [ 4 ] and often called the Poincaré disk model . The figure below shows the conformal disc model of the hyperbolic plane which is cut into congruent triangles with angles \(\dfrac{\pi}{3}, \dfrac{\pi}{3}\), and \(\dfrac{\pi}{4}\).