A constructive approach to the quadrics of revolution using 3D dynamic geometry systems with algebraic capabilities

Roanes–Lozano, Eugenio

doi:10.1002/cae.21775

Cited by 3 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To develop and implement a model which will include the best practices of the innovation cycle we will combine it with a trifocal constructive approach . This model is combination of Unified process model as highly effective management tool and Constructive education model as a deductive learning tool . The general approach of this system consists from three distinctive phases: planning, implementation, and learning.…”

Section: Methodsmentioning

confidence: 99%

E‐learning engineers based on constructive and multidisciplinary approach

Pećanin¹,

Spalević²,

Mekić

et al. 2019

Comp Applic In Engineering

View full text Add to dashboard Cite

In this study, we applied constructive approach to education supplemented with the innovation cycle approach. The main goal is to develop the innovative ideas from a clear start up to the implementation phase. Since multiple ideas tackle multidisciplinary problems, to properly present all needed concepts we used teachers from different fields of science. This was implemented through a pilot project and all results were assessed using a quasi experimental approach and constructive qualitative methodology to show the increase of interest with students in the areas of innovation, constructivism, and multidisciplinary on the cognitive, behavioral, and the affective level.

show abstract

Section: Methodsmentioning

confidence: 99%

E‐learning engineers based on constructive and multidisciplinary approach

Pećanin¹,

Spalević²,

Mekić

et al. 2019

Comp Applic In Engineering

View full text Add to dashboard Cite

show abstract

“…Here we recall some first papers [20,21] and refer to some newer reports [22,23] which emphasize the importance of connecting CAS and DGS. Since these studies, at least two important developments made them tools of increasing importance for the study of plane curves: on the one hand, the inclusion of CAS into a DGS, such as Giac in GeoGebra (see [13]), made a large category of computations feasible in the DGS itself.…”

Section: Introductionmentioning

confidence: 99%

Dynamic and automated constructions of plane curves

Dana-Picard,

Kovacs

2023

Maple Trans.

View full text Add to dashboard Cite

We provide constructions of 3 classical curves, using a new approach, based on tools for automated exploration and reasoning, especially for the determination of geometric loci. Dragging and animations are the core features in use. The different ways yield an output based either on numerical computations or on symbolic computations (these use Gröbner bases packages). These curves, which are generally presented as separate cases, appear here in a unifying frame. This work is a new contribution to the study of plane curves and to a working frame aimed at developing the dialog between different kinds of mathematical software.

show abstract

“…In fact, there are many papers on loci determination (in general) using DGS, some even applied to education [5]. This constructive approach can also be applied to quadrics using a 3D DGS [6]. This approach is somehow followed in university textbooks like [1], where conics are introduced in two steps: a first step, where only high school mathematics techniques are required, and a second one, requiring techniques introduced along the course, in order the students to be able to classify conics.…”

Section: Introductionmentioning

confidence: 99%

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

Roanes–Lozano

2017

Math.Comput.Sci.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

A constructive approach to the quadrics of revolution using 3D dynamic geometry systems with algebraic capabilities

Cited by 3 publications

References 7 publications

E‐learning engineers based on constructive and multidisciplinary approach

E‐learning engineers based on constructive and multidisciplinary approach

Dynamic and automated constructions of plane curves

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

Contact Info

Product

Resources

About