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Hyperbolic geometry

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected.

The parallel postulate in Euclidean geometry states, for two dimensions, that given a line l and a point P not on l, there is exactly one line through P that does not intersect l, i.e., that is parallel to l.

In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false.

Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid.

Note:   The above text is excerpted from the Wikipedia article "Hyperbolic geometry", which has been released under the GNU Free Documentation License.
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October 4, 2015

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