Non-Euclidean geometry

Non-Euclidean geometry is a form of geometry that rejects traditional Euclidean geometry's fifth that parallel lines extend to infinity and never intersect. There are two main forms of non-Euclidean geometry, hyperbolic and elliptic. The former allows parallel lines to intersect, the latter does not have parallel lines. In Euclidean geometry because parallel lines go on to infinity and never intersect triangles are always greater than 180 degrees, in hyperbolic geometry because parallel lines do intersect triangles are always less than 180 degrees. In elliptic geometry triangles are always greater than 180 degrees because there are no parallel lines. Non-Euclidean geometry was invented in the early nineteenth century by a Russian mathematician named Nikolai I. Lobachevsky.