This is a topic under geometry.

In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R.

(compare this with Playfair's axiom, the modern version of Euclid's parallel postulate)