A generalization of the spherical inversion. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Ramírez, José L.; Rubiano, Gustavo N.
• Is Part Of: International journal of mathematical education in science and technology. Volume 48:Issue 1(2017)
• Page Start: 132
• Page End: 149
• Publication Date: 2017-01-02
• Subjects: Primary 97G50 -- Secondary 51N20 -- 52C26; Geometry transformations -- spherical inversion -- inversion in an ellipsoid -- Pappus chain; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2016.1201598
• Languages: English
• ISSNs: 0020-739X

Abstract

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.