A generalization of the spherical inversion |
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Authors: | José L. Ramírez Gustavo N. Rubiano |
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Affiliation: | 1. Departamento de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombiajolura1@gmail.com josel.ramirez@ima.usergioarboleda.edu.co;3. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia |
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Abstract: | 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 Mathematica to generate these graphics. Finally, we generalize the Pappus chain theorem to ellipsoids. |
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Keywords: | Primary 97G50 Secondary 51N20 52C26 |
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