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In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
Numerous other constructions of both finite and infinite non-Desarguesian planes are known, see for example Dembowski (1968). All known constructions of finite non-Desarguesian planes produce planes whose order is a proper prime power, that is, an integer of the form p e , where p is a prime and e is an integer greater than 1.
In mathematics, non-Archimedean geometry [1] is any of a number of forms of geometry in which the axiom of Archimedes is negated. An example of such a geometry is the Dehn plane . Non-Archimedean geometries may, as the example indicates, have properties significantly different from Euclidean geometry .
The archetypical example is the real projective plane, also known as the extended Euclidean plane. [1] This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by PG(2, R), RP 2, or P 2 (R), among other notations.
Then the coordinate planes can be referred to as the xy-plane, yz-plane, and xz-plane. In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In that case the third coordinate may be called height or altitude.