Geometry Tutor
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Algebraic geometry and analytic geometry - In mathematics, algebraic geometry and analytic geometry are two closely related subjects. Where algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables.
Non-Euclidean geometry - The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both 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.
Birational geometry - In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension 2, the birational geometry of algebraic surfaces was largely worked out by the Italian school of algebraic geometry in the two decades on either side of the year 1900.
Absolute geometry - Absolute geometry is a geometry that does not assume the parallel postulate or any of its alternatives. Its theorems are therefore true in non-Euclidean geometries, such as hyperbolic geometry and elliptic geometry, as well as in Euclidean geometry.
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