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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 ...
While attending a geometry workshop at Cornell University about teaching geometry for university professors in 1997, Taimiņa was presented with a fragile paper model of a hyperbolic plane, made by the professor in charge of the workshop, David Henderson (designed by geometer William Thurston. [4])
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 ...
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed.The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P that are parallel to L. [1]
1829 – Bolyai, Gauss, and Lobachevsky invent hyperbolic non-Euclidean geometry, 1837 – Pierre Wantzel proves that doubling the cube and trisecting the angle are impossible with only a compass and straightedge, as well as the full completion of the problem of constructibility of regular polygons
Vladimir Grigoryevich Shukhov (Russian: Влади́мир Григо́рьевич Шу́хов; 28 August [O.S. 16 August] 1853 – 2 February 1939) was a Russian and Soviet engineer-polymath, scientist and architect renowned for his pioneering works on new methods of analysis for structural engineering that led to breakthroughs in industrial design of the world's first hyperboloid ...
Textbooks on complex functions often mention two common models of hyperbolic geometry: the Poincaré half-plane model where the absolute is the real line on the complex plane, and the Poincaré disk model where the absolute is the unit circle in the complex plane. Hyperbolic motions can also be described on the hyperboloid model of hyperbolic ...