Hyperbolic geometry - Wikipedia
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian 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.