In mathematics, non-Eucliean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to Playfair's Postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any pair of lines intersect. (See the entries on hyperbolic geometry and elliptic geometry for more information.)