The disk model of hyberolic geometry is made to map hyperbolic 2 space (which is infinite in area) into the finite interior of the disk. In order to capture thi

The disk model of hyberolic geometry is made to map hyperbolic 2 space (which is infinite in area) into the finite interior of the disk. In order to capture this, the normal euclidean notion of distance is distorted by a function which allows "distances" to go to infinity as a curve approaches the boundary of the disk.