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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.
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Computers & Math News
December 26, 2025
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Dec. 5, 2025 Scientists have discovered how to electrically power insulating nanoparticles using organic molecules that act like tiny antennas. These hybrids generate extremely pure near-infrared light, ideal for ...
Dec. 5, 2025 A researcher from the University of Tokyo and a U.S.-based structural engineer developed a new computational form-finding method that could change how architects and engineers design lightweight and ...
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