A generalization of the spherical inversion
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José L. Ramírez [1] ; Gustavo N. Rubiano [2]
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[1] Universidad Sergio Arboleda
Universidad Sergio Arboleda
Colombia
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[2] Universidad Nacional de Colombia
Universidad Nacional de Colombia
Colombia
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 1, 2017, págs. 132-149
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images of planes, spheres, ellipsoids and other curves. We use the software Mathematicato generate these graphics. Finally, we generalize the Pappus chain theorem to ellipsoids.
