non-euclidean geometry

In mathematics, non-Euclidean 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 stating 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.)
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Noun
1. geometry based on axioms different from Euclid's
(hypernym) geometry
(hyponym) hyperbolic geometry