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A brief note on the approach to the conic sections of a right circular cone from dynamic geometry

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Roanes–Lozano, Eugenio (2017) A brief note on the approach to the conic sections of a right circular cone from dynamic geometry. Mathematics in Computer Science, 11 (3-4). 439 -448. ISSN 1661-8289

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Official URL: https://link.springer.com/article/10.1007/s11786-017-0307-3



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 implicitequation of the conic.


Item Type:Article
Uncontrolled Keywords:Geometría dinámica, Cónicas
Palabras clave (otros idiomas):Conics, Dynamic Geometry, 3D Geometry, Computer Algebra
Subjects:Sciences > Mathematics > Algebra
Sciences > Mathematics > Geometry
ID Code:47806
Deposited On:29 May 2018 14:47
Last Modified:30 May 2018 07:56

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