The Study of Ellipses and Hyperbolas As Second order Curves Using Geogebra 4

Trifunov, Zoran and Stojanovska, Linda (2011) The Study of Ellipses and Hyperbolas As Second order Curves Using Geogebra 4. In: Proceedings of the Eighth Conference on Informatics and Information Technology. Institute of Informatics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia, Skopje, Macedonia, pp. 155-158. ISBN 978-9989-668-90-6


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In the third year of middle school (11th grade), pupils are introduced to circles, ellipses, hyperbolas and parabolas as second order curves or conic sections. These curves are not studied in depth. However, they have great significance in the arts and sciences and we can use this to increase interest. In this paper, we demonstrate ways to give physical meaning to ellipses and hyperbolas. We then use the freeware GeoGebra 4.0 to virtualize and visualize this process. With this version there are greater possibilities for working with these curves. We can input all of their different definitions starting with the canonical (implicit) equations and then dynamically show how and why the definitions coincide. Finally, we demonstrate a project in which pupils/students use GeoGebra to build a simulator of a natural phenomenon that generates hyperbolas.

Item Type: Book Section
Subjects: International Conference on Informatics and Information Technologies > eWorld - eWork, eCommerce, eBusiness, eLearning
Depositing User: Vangel Ajanovski
Date Deposited: 28 Oct 2016 00:15
Last Modified: 28 Oct 2016 00:15

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