The cone and conics (Q2721284)

Translation of the Spanish summary: Hipocrat of Chios (460 b.C.) obtained some equations, which in a later time (350 b.C.) Menecmo related to some conic sections. Since then, the curves obtained by cutting a cone with a plane have been considered in many domains of mathematics and general sciences. NEWLINENEWLINENEWLINEWith analytic geometry new tools were created for the analysis of these curves which we today classify as circumference, ellipse, parabola and hyperbola. NEWLINENEWLINENEWLINEIn this paper we give an introduction to this matter for students and teachers of geometry. We consider some historic developments and also in which kind of problems these curves are involved.NEWLINENEWLINENEWLINEUsing the famous construction of Dandelin we also deduce some geometric properties of these curves.NEWLINENEWLINEFor the entire collection see [Zbl 0948.00027].