kinematic geometries also called non euclidean geometry essential difference metric geometries nature parallel lines euclid 's fifth postulate parallel postulate equivalent playfair 's postulate states within two dimensional plane given line point ''a'' exactly one line ''a'' intersect hyperbolic geometry contrast infinitely many lines ''a'' intersecting elliptic geometry line ''a'' intersects another way describe differences
Formal science Mathematics Pure mathematics Geometry Non-Euclidean geometry