non-Euclidean

[ non-yoo-klid-ee-uhn ]

adjective

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

non-Euclidean

/ nŏn′yo̅o̅-klĭd′ē-ən /

1. 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 .
2. Compare Euclidean

Word History and Origins

Origin of non-Euclidean¹

First recorded in 1870–75

Example Sentences

At its best, cosmic horror makes viewers feel as if they are tiny, powerless creatures facing something — a being, a concept, Lovecraft’s beloved non-Euclidean geometry — whose scope is so great that it is disconcertingly, disturbingly hard to grasp.

From New York Times

The emergence in the early nineteenth century of “non-Euclidean” geometry was a watershed for mathematics in that it described a theory of physical space that totally contradicted our experience of the world and therefore was hard to imagine, but nevertheless contained no mathematical contradictions, and so was as mathematically valid as the Euclidean system that came before.

From Literature

Non-Euclidean geometry and Cantor’s set theory were gateways into strange and wonderful worlds, and I’ll visit them both in the following pages.

From Literature

Riemann’s lecture, given in 1854, consolidated the paradigm shift in our understanding of geometry resulting from the fall of the parallel postulate, by establishing an all-embracing theory that included the Euclidean and non-Euclidean within it.

From Literature

When a surface has positive or negative curvature, it is curved, or non-Euclidean, and the results of The Elements do not hold.

From Literature