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Nikolai Ivanovich Lobachevsky (Russian: Никола́й Ива́нович Лобаче́вский, IPA: [nʲɪkɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕefskʲɪj] ⓘ; 1 December [O.S. 20 November] 1792 – 24 February [O.S. 12 February] 1856) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for ...
Compared to Euclidean geometry, hyperbolic geometry presents many difficulties for a coordinate system: the angle sum of a quadrilateral is always less than 360°; there are no equidistant lines, so a proper rectangle would need to be enclosed by two lines and two hypercycles; parallel-transporting a line segment around a quadrilateral causes ...
János Bolyai (Hungarian: [ˈjaːnoʃ ˈboːjɒi]; 15 December 1802 – 27 January 1860) or Johann Bolyai, [2] was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the ...
Hungarian mathematics began its rise to prominence in the early 1800s with János Bolyai, one of the creators of non-Euclidean geometry, and his father Farkas Bolyai. Though they were largely ignored during their lifetimes, János Bolyai's groundbreaking work on hyperbolic geometry would later be recognized as foundational to modern mathematics.
Motivated by the work of Schweikart, Taurinus examined the model of geometry on a "sphere" of imaginary radius, which he called "logarithmic-spherical" (now called hyperbolic geometry). He published his "theory of parallel lines" in 1825 [R 1] and "Geometriae prima elementa" in 1826. [R 2] [2] For instance, in his "Geometriae prima elementa" on ...
1975 – Benoit Mandelbrot, fractals theory, 1981 – Mikhail Gromov develops the theory of hyperbolic groups, revolutionizing both infinite group theory and global differential geometry, 1983 – the classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
In 1913 and 1914 he bridged the gap between hyperbolic geometry and special relativity with expository work. For instance, his book Introduction Géométrique à quelques Théories Physiques [ 8 ] described hyperbolic rotations as transformations that leave a hyperbola stable just as a circle around a rotational center is stable.
Hyperbolic theory may refer to: Hyperbolic geometry; The theory of hyperbolic partial differential equations This page was last edited on 4 ...