Resultado de búsqueda
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or diameters of the unit circle.
El modelo de semiplano de Poincaré lleva el nombre de Henri Poincaré, pero se originó con Eugenio Beltrami, quien lo utilizó, junto con el modelo de Klein y el modelo de disco de Poincaré, para demostrar que la geometría hiperbólica era equiconsistente con la geometría euclidiana.
3 de sept. de 2013 · Poincaré established a famous dictionary translating concepts and propositions of Lobachevskii’s geometry into Euclidean geometry in order to create a model to show the relative consistency of Lobachevskii’s geometry (Poincaré 1891: 771; cf. 1902: 68; 2017: 37).
The Poincaré disk model for hyperbolic geometry is the pair (D,H) where D consists of all points z in C such that |z|<1, and H consists of all Möbius transformations T for which T(D)=D.…
The second model that we use to represent the hyperbolic plane is called the Poincaré disk model, named after the great French mathematician, Henri Poincaré (1854 - 1912). This model is constructed starting from the previous one.
16 de may. de 2024 · Henri Poincaré was a French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics.
His disc model of non-Euclidean geometry closely resembles Riemann’s; he himself explained how it is related to Beltrami’s. We look at the correspondence between Poincaré and Klein in 1881–1882, and a long series of exercises develops the basic properties of the Poincaré disc.
