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Of, relating to, or being any of several modern geometries that are not based on the postulates of Euclid.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


(ˌnɒn yuˈklɪd i ən)

differing from the postulates of Euclid or based upon postulates other than those of Euclid: non-Euclidean geometry.
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References in classic literature ?
This distinguished scientist has expounded his views in a book entitled "Verschwinden und Seine Theorie," which has attracted some attention, "particularly," says one writer, "among the followers of Hegel, and mathematicians who hold to the actual existence of a so- called non-Euclidean space--that is to say, of space which has more dimensions than length, breadth, and thickness--space in which it would be possible to tie a knot in an endless cord and to turn a rubber ball inside out without 'a solution of its continuity,' or in other words, without breaking or cracking it."
And the end which the individual subjects, the agents of the undertaking, pursued in reality was always the same: to refute the possibility of a non-Euclidean world -- the intellectual annihilation before birth of a world which ab initio only represented for everybody -- whether geometricians or not -- the evident impossibility of itself.
DiZerega's introduction to non-Euclidean politics came at the YAF chapter's third meeting, when a beautiful young woman--perhaps Decker, though diZerega doesn't identify her--arrived and sat in the back of the room.
But in a non-Euclidean universe, the same rules do not apply.
And though chaos theory, non-Euclidean geometry, physics, and contemporary cosmology provide trajectories for much of the work here, Waldrop's "crow does not fly as the crow flies" (28).
It has semi-metric (non-Euclidean) properties but is generally acknowledged to be a good measure of ecological distance for species abundances (Faith et al.
(In non-Euclidean, curved-space geometries this postulate does not hold true.)
Then Section 2.3 describes the algorithm for Euclidean TSP in [R.sup.d] and Section 2.4 describes the (trivial) extensions of our algorithm when distances are measured in some non-Euclidean norms.
Second, he pointed out that non-Archimedean continua cannot be excluded on empirical or logical grounds: non-Archimedean geometry, in which Archimedes' axiom is denied, is just as legitimate as non-Euclidean geometry, in which Euclid's fifth postulate is denied.
In the context of pure mathematics before the discovery of non-Euclidean spaces, sentence (EU) was held true.
Klein, investigations of motion of the rigid body (the kinetic analogue of the elastic problem) in non-Euclidean spaces were done by Clifford as early as 1874 ([9]; p.