Exploring Geometrical Content with ICTs: A Case Study on Infinitesimal Bending of a Hyperbolic Paraboloid

10th International Scientific Conference Technics, Informatics and Education – TIE 2024, str. 140-143

АУТОР(И) / AUTHOR(S): Miroslav Maksimović , Marija Najdanović , Eugen Ljajko , Nataša Kontrec

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DOI: 10.46793/TIE24.140M

САЖЕТАК /ABSTRACT:

Information and Communication Technologies (ICTs) usage is of great importance in development of mathematics in general and geometry in particular. Software packages can, for instance, be helpful in differentiation and integration, as well as for solving complex numerical problems, which can be time-consuming if done without ICTs.  Instruction of geometrical content at any level often requires usage of the content’s graphic representation. For that purpose, software packages for geometrical content visualization are used. Here we present an example where the computer usage in geometrical content exploration is shown. Visualization is especially important in the infinitesimal bending theory. In the paper we examine infinitesimal bending of a curve on the hyperbolic paraboloid and determine the infinitesimal bending field that leaves the bent curves on it. Since two such fields are obtained, we use Mathematica software package for representation of the curve and observe the impact both fields have on it. We also determine the bending field that leaves the curve on the hyperbolic paraboloid with a given precision

КЉУЧНЕ РЕЧИ / KEYWORDS: 

infinitesimal bending; hyperbolic paraboloid; visualization; geometry education; Mathematica

ПРОЈЕКАТ / ACKNOWLEDGEMENTS:

This research was supported by the research by project no. 451-03-65/2024-03/200123 of the Ministry of Education, Science and Technological Development of the Republic of Serbia and by internal-junior project IJ-2303 of Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica.

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