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Article

Visualizing a Cubic Linkage through the Use of CAS and DGS

by 1,*,†, 2,†, 3,† and 4,†
1
Departamento de Ingeniería Industrial, Escuela Politécnica Superior, Universidad Antonio de Nebrija, 28015 Madrid, Spain
2
Sociedad Asturiana de Educación Matemática “Agustín de Pedrayes”, Federación Española de Sociedades de Profesores de Matemáticas, 33213 Gijón, Spain
3
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39008 Santander, Spain
4
CEAD Profesor Félix Pérez Parrilla, 35005 Las Palmas de Gran Canaria, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Yang-Hui He
Mathematics 2022, 10(15), 2550; https://doi.org/10.3390/math10152550
Received: 22 June 2022 / Revised: 18 July 2022 / Accepted: 20 July 2022 / Published: 22 July 2022
(This article belongs to the Special Issue Symbolic Computation for Mathematical Visualization)
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. View Full-Text
Keywords: dynamic geometry; geogebra; computational algebraic geometry; linkages; cube dynamic geometry; geogebra; computational algebraic geometry; linkages; cube
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MDPI and ACS Style

Recio, T.; Losada-Liste, R.; Tabera, L.F.; Ueno, C. Visualizing a Cubic Linkage through the Use of CAS and DGS. Mathematics 2022, 10, 2550. https://doi.org/10.3390/math10152550

AMA Style

Recio T, Losada-Liste R, Tabera LF, Ueno C. Visualizing a Cubic Linkage through the Use of CAS and DGS. Mathematics. 2022; 10(15):2550. https://doi.org/10.3390/math10152550

Chicago/Turabian Style

Recio, Tomás, Rafael Losada-Liste, Luis Felipe Tabera, and Carlos Ueno. 2022. "Visualizing a Cubic Linkage through the Use of CAS and DGS" Mathematics 10, no. 15: 2550. https://doi.org/10.3390/math10152550

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