1) Hyperbolic geometry 
In hyperbolic geometry, a horocycle (ὅριον + κύκλος — border + circle) is a curve whose normal geodesics all converge asymptotically. (It is also called an oricycle or oricircle, and a limit circle.) It is the two-dimensional example of a horosphere (or orisphere). A horocycle can also be described as the limit of the circles that sh...