Lobachevsky


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Lobachevsky

Nikolai Ivanovich . 1793--1856, Russian mathematician; a founder of non-Euclidean geometry
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Corresponding Author: Anton Olegovich Ovcharov, Lobachevsky State University of Nizhni Novgorod (Nizegorodskij Gosudarstvennyj Universitet) Russia, 603950, Nizhni Novgorod, Prospekt Gagarina, 23
Antes de morir y sufriendo de ceguera, Lobachevsky publica en 1855 su Pangeometria en frances y ruso.
Lobachevsky, The new foundations of geometry with full theory of parallels [in Russian], 1835-1838, In Collected Works, V.
Taking the same partition of the Lobachevsky plane [H.
Esto se advierte claramente en los Grundlagen der Geometrie, donde "jugando" con los axiomas, Hilbert obtiene numerosos resultados: geometrias no arquimedianas, nuevos teoremas acerca de la continuidad, una nueva caracterizacion topologica del plano, una caracterizacion de la geometria euclidiana y de la geometria de Bolyai y Lobachevsky mediante grupos de desplazamientos, un analisis del papel de los teoremas de Desargues y de Pascal en la coordenatizacion del espacio, un estudio comparativo de las distintas geometrias entre si, y una investigacion de los medios requeridos para demostrar ciertos teoremas.
Lobachevsky cotejo observaciones astronomicas para determinar la constante de su geometria.
Lobachevsky (1792-1856) matematico ruso que construyo una
25) The thesis with which Lobachevsky decisively changed scientific perceptions of space challenged the Euclidean axiom that two parallel lines never meet; positing that this principle was valid only if the lines were projected on a straight plane, he demonstrated that a curved plane, such as the earth's surface, would actually result in the unification of the parallel lines.
Angell, (3) and others (4) with discovering non-Euclidean geometry over half a century before the mathematicians--sixty years before Lobachevsky and ninety years before Riemann.
The concrete example is the discovery of non-Euclidean geometries, about which it is argued that some of the hypotheses created by Lobachevsky were indeed image based, something that helped to deal with the fifth parallel postulate by manipulation of symbols.
The adverse hypothesis which had motivated Saccheri's desperate campaign was the equivalent of the most paradoxical of all of Geminus' theorems -- and in his commentary Saccheri was to give it a formulation which was almost identical, word for word, to an axiomatic proposition on which Lobachevsky was later to construct his non-Euclidean geometry.