Within contemporary geometry there are many kinds of geometry that are quite different from Euclidean geometry, first encountered in the forms of elementary geometry, plane geometry of triangles and circles, and solid geometry. The conventional meaning of Non-Euclidean geometry is the one set in the nineteenth century: the fields of elliptic geometry and hyperbolic geometry created by dropping the parallel postulate. These are very special types of Riemannian geometry, of constant positive curvature and constant negative curvature respectively.
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