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Of, relating to, or being any of several modern geometries that are not based on the postulates of Euclid.


(ˌnɒn yuˈklɪd i ən)

differing from the postulates of Euclid or based upon postulates other than those of Euclid: non-Euclidean geometry.
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.
To conclude, he introduces non-Euclidean geometry and curvature, and explains why it is called hyperbolic.
This non-Euclidean electoral geometry was most famously employed on behalf of Bill Clinton decades ago by his feminist supporters, who were willing to dismiss behavior ranging from a voluntary affair with an intern to much more serious allegations of rape and assault, because they believed he would defend women's rights more effectively than his would-be replacements.
In week 11, along with non-Euclidean geometry the interactions of mathematics with art, literature, science and philosophy were addressed via the symmetry and mathematical theory used in the drawings of the Dutch artist M.
4) To demolish Einstein's theories of relativity (in elliptic geometry), you could go back and prove the parallel postulate, bringing down not only Einstein, but all of the non-Euclidean geometries, as well.
For our local geometry, in which our immediate environment and our cognitive constitution cooperate more simply than they would in Non-Euclidean spaces, seems to put us uniquely in medias res, uniquely placed for the inquiry into our Beyond.
To understand its defining characteristics in greater depth we study them in Euclidean geometry and in a particular non-Euclidean geometry system known as 'taxicab geometry'.
Kant's critical philosophy, perhaps the only serious rival to realism in the minds of some scientists, crashed and burned in the nineteenth century with the development of non-Euclidean geometries and their later incorporation into the non-Newtonian physics of relativity in the early twentieth century.
Smarandache introduced the degree of negation of an axiom or of a theorem in geometry: Smarandache geometries (1969), which can be partially Euclidean and partially non-Euclidean.
Pendulum-like pieces reminiscent of Lescher's earlier work hung in the back; a polished metallic spear-like form jutted down from the ceiling and others pierced the wall; the non-Euclidean form of a flat basalt floor piece with relaxed metric requirements that do not form a perfect figure eight was highlighted by the work's title, Nao Euclidiana, 2013; on the back wall was Livro (Book), 2013, two jacaranda-wood blocks with a thin strip of brass shining between them.
Where, in response to such criticisms, Latour (1999) lamented the inaptness of its rendering of the original French, proffering "actant-rhizomes" as an alternative to the actor-network, Law and Mol, by contrast, responded by suggesting the necessity of "inquir[ing] into the possibility of other, non-Euclidean, non-network spatialities" (2001, page 613).
New York designer Jill Malek's Voyageur wallpaper takes non-Euclidean geometry to the next level, with a range of papers printed with lines radiating from points, like a compass gone wild.