Visualizing a Cubic Linkage through the Use of CAS and DGS

Tomás Recio, Rafael Losada-Liste, Luis Felipe Tabera and Carlos Ueno
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Tomás Recio: Departamento de Ingeniería Industrial, Escuela Politécnica Superior, Universidad Antonio de Nebrija, 28015 Madrid, Spain
Rafael Losada-Liste: Sociedad Asturiana de Educación Matemática “Agustín de Pedrayes”, Federación Española de Sociedades de Profesores de Matemáticas, 33213 Gijón, Spain
Luis Felipe Tabera: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39008 Santander, Spain
Carlos Ueno: CEAD Profesor Félix Pérez Parrilla, 35005 Las Palmas de Gran Canaria, Spain

Mathematics, 2022, vol. 10, issue 15, 1-29

Abstract: Our goal is to discuss the different issues that arise when attempting to visualize a joints-and-bars cube through GeoGebra, a widespread program that combines dynamic geometry (DGS) and computer algebra systems (CAS). As is standard in the DGS framework, the performance of the graphic model (i.e., the positions of the other vertices when dragging a given one) must correspond to a mathematically rigorous, symbolic computation-driven output. This requirement poses both computational algebraic geometry and dynamic geometry programming challenges that will be described, together with the corresponding proposed solutions. Among these, we include a complete determination of the dimension of the cubic linkage from an algebraic perspective, and introduce advanced 3D visualizations of this structure by using the GeoGebra software.

Keywords: dynamic geometry; geogebra; computational algebraic geometry; linkages; cube (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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