A generalization of the spherical inversion

José L. Ramírez ^[1] ; Gustavo N. Rubiano ^[2]
1. [1] Universidad Sergio Arboleda
  
  Universidad Sergio Arboleda
  
  Colombia
2. [2] Universidad Nacional de Colombia
  
  Universidad Nacional de Colombia
  
  Colombia
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 1, 2017, págs. 132-149
Idioma: inglés
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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.