Modeling the Cube Using Geogebra

Visualizing a Cubic Linkage through the Use of CAS and DGS

“…Throughout this work, we have addressed some open questions that (at least to our knowledge) first appeared in the last section of [10] and which will help us to summarize our contributions by quoting them and updating their current status: (i) "Yet, we have to report that some jumps occur between isomer positions, near singular placements. For instance, when a = 270 • , the parallelogram AOBU collapses.…”

“…We will see in the sequel the difficulties that arise when trying to fully understand its geometry, even with powerful mathematical software such as Maple. Indeed, two of the authors already approached the study of this elusive structure in a previous work [10], stating some open questions which we partially solve here.…”

“…When trying to model linkages in DGS such as GeoGebra, some difficulties arise when trying to imitate the behaviour that these mechanisms show in physical constructions. One of these difficulties has to do with the order in which the steps in a geometric construction are performed (see also [10] for a similar discussion). As an example, let us consider the construction of a square linkage OUFE on the plane (see Figure 11) using GeoGebra.…”

“…Then, in Section 4, after discussing some issues concerning the visualization of linkages in DGS, we proceed to describe some of the visual, dynamic models we have developed in GeoGebra to simulate the cube in a 3D environment. Finally, we conclude by presenting how our approach contributes to answering a number of questions posed in [10]. These questions spurred our interest to delve deeper into this structure, which to us represents a real challenge both to completely understand its underlying algebraic structure as well as to visually modelize it through the use of DGS.…”

Teachers’ Perceptions toward the use of GeoGebra in the Teaching and Learning of Mathematics

“…In addition, GeoGebra software is designed for use in schools and educational institutions (Hohenwarter, 2004). GeoGebra is a versatile software, able to generate a picture or graphic visualization of mathematical ideas or concepts (Hohenwarter and Jones, 2007) and to display a picture or graphic on the simultaneous visualization of the window graphics, algebra and geometry (Arranz et al, 2009). Teachers also reported that GeoGebra software can generate dynamic visualizations in teaching students a particular calculus concept.…”