A Brief Note on the Approach to the Conic Sections of a Right Circular Cone from Dynamic Geometry

Abstract

Abstract. Nowadays there are different powerful 3D dynamic geometry systems (DGS) such as GeoGebra 5, Calques 3D and Cabri Geometry 3D. An obvious application of this software that has been addressed by several authors is obtaining the conic sections of a right circular cone: the dynamic capabilities of 3D DGS allows to slowly vary the angle of the plane w.r.t. the axis of the cone, thus obtaining the different types of conics. In all the approaches we have found, a cone is firstly constructed and it is cut through variable planes. We propose to perform the construction the other way round: the plane is fixed (in fact it is a very convenient plane: z = 0) and the cone is the moving object. This way the conic is expressed as a function of x and y (instead of as a function of x, y and z). Moreover, if the 3D DGS has algebraic capabilities, it is possible to obtain the implicit equation of the conic.

Cabri 3D Kullanımının Öğretmen Adaylarının Analitik Geometri Başarılarına Etkisinin İncelenmesi

“…Nitekim, geometrik kavramları anlamlandırma (Tapan-Broutin, 2010), somut ve soyut çalışma alanları arasındaki geçişler (Salazar, 2018;Wares, 2018), muhakeme ve ispat becerilerini geliştirmek (Pedemonte, 2018) amacıyla pek çok öğretim materyali geliştirilmiştir. Araştırmalar bilgisayar yazılımlarının bu anlamda önemli bir görev üstlenme potansiyelinin bulunduğunu göstermektedir (Assude, 2017;Roanes-Lozano, 2017;Soury-Lavergne, 2017;Trocki ve Hollebrands, 2018).…”