[size=150]In this geometry we impose the condition that for each point outside a straight line more than one parallel can pass to it. In fact, there will be infinite parallel lines to a given one. If the lines intersect at infinity, we will say that they are parallel, but if they do not even intersect there, then we will say that they are ultraparallel.[br][br]A triangle in this geometry has angles that always add less than 180º.[/size]

[size=150]There are 3 models that can be represented in the Euclidean plane for this geometry. They are first devised by Beltrami. The 3 models are:[br][br][list][*]Poincaré Disk[br][/*][*]Klein Disk[br][/*][*]Upper Halfplane[/*][/list][br]We will first use the Poincaré Disk model. This model is conformal (it respects the value of angles in original space), although it isn't isometric (it distorts the distances between points in original and the model).[/size]