English: In the Poincaré disc model of the hyperbolic plane, lines are represented by circular arcs orthogonal to the boundary of the closure of the disc. The thin black lines meet at a common point and do not intersect the thick blue line, illustrating that in the hyperbolic plane there are infinitely many lines parallel to a given line passing through the same point. [License: as the sole author of this image, I hereby release it into the public domain.]