Resumen de Transformación que alinea los centros de tres esferas preservando tangencias

Eugenio Roanes Macías , Eugenio Roanes Lozano

• Given three spherical surfaces with non-collinear centers, we try to find a transformation that converts them into spherical surf aces whose centers are collinear points and such that tangency is preserved, if applies. That an inversion-type transformation satisfying these conditions exists is proven. A synthetic geometry constructive method to determine such a transformation, appliable when the three given spherical surfaces satisfy certain conditions, is shown. Moreover, preserving tangent surfaces propriety makes this transformation very useful for solving configuration problems involving spherical surfaces. Finally, an algorithm to implement this method on Computer Algebra Systems is also provided.