Примери коришћења Non-euclidean на Енглеском и њихови преводи на Српски
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From the early 1800's Gauss had an interest in the question of the possible existence of a non-Euclidean geometry.
Jean Metzinger andAlbert Gleizes wrote with reference to non-Euclidean geometry in their 1912 manifesto, Du"Cubisme".
Or there's the non-Euclidean work of Bernhard Riemann in the 1850s, which Einstein used in the model for general relativity a century later.
Indicating that he had known of the existence of a non-Euclidean geometry since he was 15 years of age(this seems unlikely).
Omar's attempt was a distinct advance, and his criticisms made their way to Europe, andmay have contributed to the eventual development of non-Euclidean geometry.
In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate,[16].
This allows for parallel mathematical theories built on alternate sets of axioms(see Axiomatic set theory and Non-Euclidean geometry for examples).
He was a Hungarian mathematician, one of the founders of non-Euclidean geometry- a geometry that differs from Euclidean geometry in its definition of parallel lines.
This property does not hold in general, even if the space is two-dimensional(but non-uniformly convex, and,in particular, non-Euclidean) and the sites are points.
János Bolyai or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry- a geometry that differs from Euclidean geometry in its definition of parallel lines.
Khayyam's attempt was a distinct advance, and his criticisms made their way to Europe, andmay have contributed to the eventual development of non-Euclidean geometry.
Since then, and into modern times,geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
In a book review in 1816he discussed proofs which deduced the axiom of parallels from the other Euclidean axioms,suggesting that he believed in the existence of non-Euclidean geometry, although he was rather vague.
It was argued that Cubism itself was not based on any geometrical theory, but that non-Euclidean geometry corresponded better than classical, or Euclidean geometry, to what the Cubists were doing.
There is no longer an assumption that axiomsare"true" in any sense; this allows for parallel mathematical theories built on alternate sets of axioms(see Axiomatic set theory and Non-Euclidean geometry for examples).
In Du"Cubisme" Metzinger argued that Cubism itself was not based on any geometrical theory, but that non-Euclidean geometry corresponded better than classical geometry to what the Cubsists were doing.
This insight had the corollary that non-Euclidean geometry was consistent if and only if Euclidean geometry was, giving the same status to geometries Euclidean and non-Euclidean, andending all controversy about non-Euclidean geometry.
Cubism itself, then, was not based on any geometrical theory, butcorresponded better to non-Euclidean geometry than classical or Euclidean geometry.
Henri Poincaré, one of the father's of non-Euclidean geometry, believed that the existence of non-Euclidean geometry, dealing with the non-flat surfaces of hyperbolic and elliptical curvatures, proved that Euclidean geometry, the long standing geometry of flat surfaces, was not a universal truth, but rather one outcome of using one particular set of game rules.
The geometry of the space depends on the metric chosen, andby using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.
Many axiomatic systems were developed in the nineteenth century,including non-Euclidean geometry, the foundations of real analysis, Cantor's set theory, Frege's work on foundations, and Hilbert's'new' use of axiomatic method as a research tool.