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Denying or going beyond Euclidean principles in geometry, especially contravening the postulate that only one line through a given point can be parallel to a given line.
‘It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well.’
‘Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate.’
‘A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry.’
‘By chapter two he is proving Pythagoras' theorem from first principles and introducing non-Euclidean geometry.’
‘In 1915, Albert Einstein found it more convenient, the conventionalist would say, to develop his theory of general relativity using non-Euclidean rather than Euclidean geometry.’