Poincaré disk model

The Poincaré disk is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk. In this applet you can check some theorems well known from Euclidean geometry that they also hold in Poincaré's model. Also you can switch Escher's Circle limit III woodcut on to play covering a triangle and learn more about regular triangles in hyperbolic geometry. By dragging the point U it is possible to change the length of the unit. The original version of this applet was created by Lajos Szilassi. An extension of this demonstration is planned to be published in the near future: a set of GeoGebra tools will be provided to explore hyperbolic geometry even more.