Klein Disk
The Klein Disk is a non-conformal model of the hyperbolic plane. Later it was discovered that Beltrami independently had discovered this model.
A couple experiments for which you can use this:
-see how distance works on the disk by moving P & Q
-investigate a Klein circle by tracing Q and trying to keep the distance constant.
-turn on the 3rd point and try to make an equilateral triangle
-turn on the perpendicular through R to AB to investigate right angles in this model