The debate that eventually led to the discovery of non-Euclidean geometries began almost as soon as Euclid's work Elements was written. While Euclidean geometry, named after the Hellenistic Egyptian mathematician Euclid, includes some of the oldest known mathematics, non-Euclidean geometries were not widely accepted as legitimate in the Western world until the 19th century. The Mobius strip and Klein bottle are both complete one-sided objects, impossible in a Euclidean plane. The concepts applied to certain non-Euclidean planes can only be shown in three dimensions. Non-Euclidean geometries and in particular elliptic geometry play an important role in relativity theory and the geometry of spacetime. In addition, elliptic geometry modifies Euclid's first postulate so that two points determine at least one line.īasing new systems on these assumptions, each is constructed with its own rules and postulates. In elliptic geometry there are no lines that will not intersect, as all that start separate will converge. In hyperbolic geometry there are many more than one distinct line through a particular point that will not intersect with another given line. In general, there are two forms of non-Euclidean geometry, hyperbolic geometry and elliptic geometry. Non-Euclidean geometry systems differ from Euclidean geometry in that they modify Euclid's fifth postulate, which is also known as the parallel postulate.
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