non-Euclidean

[ non-yoo-klid-ee-uhn ]

Phonetic (Standard)IPA

adjective

differing from the postulates of Euclid or based upon postulates other than those of Euclid.

non-Euclidean

/ nŏn′yo̅o̅-klĭd′ē-ən /

Relating to any of several modern geometries that are based on a set of postulates other than the set proposed by Euclid, especially one in which all of the postulates of Euclidean geometry hold except the parallel postulate .
Compare Euclidean

First recorded in 1870–75

The real basis of the non-Euclidean geometry is dimension as direction.

But they constitute the substance of non-Euclidean geometry; they are its blood and sinews.

Lobachevski has proved not, by creating non-Euclidean geometry.

Permit me for brevity to call such a movement a non-Euclidean displacement.

But it is not enough that the Euclidean (or non-Euclidean) geometry can never be directly contradicted by experience.

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