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- Los modelos de geometría no euclidiana son modelos matemáticos de geometría que no cumplen el quinto postulado de Euclides, el que establece que dos rectas paralelas son equidistantes. En los modelos geométricos hiperbólicos (geometría hiperbólica), dos rectas paralelas son divergentes; y en modelos geométricos elípticos (geometría elíptica), no existen líneas paralelas que pasen por un punto exterior. La geometría euclidiana se fundamenta en la noción de "plano euclidiano". El equivalente en geometría elíptica es una esfera, donde las líneas son circunferencias (por ejemplo la línea del ecuador o los meridianos del globo terráqueo), y puntos opuestos uno del otro son identificados (considerados ser el mismo). La pseudoesfera tiene la curvatura apropiada para modelar la geometría hiperbólica. (es)
- Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A parallel to l, and in elliptic geometric models, parallel lines do not exist. (See the entries on hyperbolic geometry and elliptic geometry for more information.) Euclidean geometry is modelled by our notion of a "flat plane." The simplest model for elliptic geometry is a sphere, where lines are "great circles" (such as the equator or the meridians on a globe), and points opposite each other are identified (considered to be the same). The pseudosphere has the appropriate curvature to model hyperbolic geometry. (en)
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- 1562 (xsd:nonNegativeInteger)
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- Los modelos de geometría no euclidiana son modelos matemáticos de geometría que no cumplen el quinto postulado de Euclides, el que establece que dos rectas paralelas son equidistantes. En los modelos geométricos hiperbólicos (geometría hiperbólica), dos rectas paralelas son divergentes; y en modelos geométricos elípticos (geometría elíptica), no existen líneas paralelas que pasen por un punto exterior. (es)
- Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A parallel to l, and in elliptic geometric models, parallel lines do not exist. (See the entries on hyperbolic geometry and elliptic geometry for more information.) (en)
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- Modelos de geometría no euclidiana (es)
- Models of non-Euclidean geometry (en)
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