geometry based upon one or more postulates that differ from those of Euclid, especially from the postulate that only one line may be drawn through a given point parallel to a given line.
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British Dictionary definitions for non-euclidean geometry
the branch of modern geometry in which certain axioms of Euclidean geometry are restated. It introduces fundamental changes into the concept of space
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012