Achievements and Challenges in Automatic Locus and Envelope Animations in Dynamic Geometry

Kovács, Zoltán

doi:10.1007/s11786-018-0390-0

Cited by 11 publications

(7 citation statements)

References 8 publications

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“…For this reason, studying circle theorems, particularly in teacher training institutions, need more creative techniques that will improve pre-service teachers' circle theorems comprehension and skills (Amevor & Bayaga, 2021;Kwadwo & Asomani, 2021;Tay & Wonkyi, 2018). Some of these novel ways that are recognized to aid learners' knowledge of circle theorems include the use of educational technology, notably the incorporation of mathematics software into the teaching and learning of circle theorems (Amevor & Bayaga, 2021;Kovács, 2018;Tay & Wonkyi, 2018). GeoGebra is a popular mathematics application software in the teaching and learning of circle theorems (Adhikari, 2021;Arbain & Shukor, 2015;Tay & Wonkyi, 2018).…”

Section: Introductionmentioning

confidence: 99%

Acceptance of the GeoGebra Application in Learning Circle Theorems

Philemon

Chibisa

Mabusela

2022

IJLTER

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The learning area of circle theorems is one of the most difficult topics in geometry, resulting in low student performance. GeoGebra has been shown in studies to enhance learners' proficiency in circle theorems. However, pre-service teachers' use of GeoGebra is not at the expected level in Eswathini. The adoption of an information system is reliant on its acceptance by individuals. However, little is known regarding pre-service teachers' use of GeoGebra to understand circle theorems. The goal of this study was to investigate pre-service teachers' perceptions of GeoGebra's suitability for learning circle theorems. A cross-sectional survey design was used in this investigation, with a total of 187 pre-service instructors as participants. The model explained 74.9% of the variance in the acceptability of GeoGebra for learning circle theorems by Eswatini pre-service teachers. According to the findings, task-technology fit, system quality, system compatibility, perceived ease of use, perceived usefulness, perceived attitude toward, and user satisfaction account for 74.9% of the variance in actual use. The study's findings revealed that rural Eswatini pre-service teachers' reported attitude toward using the mathematics software application GeoGebra for learning circle theorems was the strongest direct predictor of actual use. This research shows that pre-service teachers' views toward technology integration in education should be positive for educational learning applications to be successfully adopted in Eswatini teacher training institutes.

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Section: Introductionmentioning

confidence: 99%

Acceptance of the GeoGebra Application in Learning Circle Theorems

Philemon

Chibisa

Mabusela

2022

IJLTER

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“…We can verify this fact by opening the CAS View and issue the command Factors(LeftSide(eq2)-RightSide(eq2)) which informs us that the obtained result consists of two factors: one defines a circle with center (0, 0) and radius 1/2, reported as 4x We emphasize here that, in the background, the analytic method was used by GeoGebra, that is, computing a Jacobi determinant and then using elimination to obtain an equation in two variables, defining a plane curve. (See [14] and [15] for more details.) In other words: GeoGebra performed an automated proof on the validity of the formula that describes O 1/2 (x, y).…”

Section: Symbolic Experiments With Geogebramentioning

confidence: 99%

Automated Study of a Regular Trifolium

Dana-Picard

2018

Math.Comput.Sci.

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The non-uniqueness of a rational parametrization of a rational plane curve may influence the process of computing envelopes of 1-parameter families of plane curves. We study envelopes of family of circles centred on a regular trifolium and its offsets, paying attention to different parametrizations. We use implicitization both to show that two rational parametrizations of a curve are equivalent, and to determine an implicit equation for the envelope under study. The derivation of an implicit equation of an offset follows another path, leading to new developments of the package GeoGebra Discovery. As an immediate symbolic result, we obtain that in the general case the offset curve of a regular trifolium is an algebraic curve of degree 14. We illustrate this fact by providing a GeoGebra applet that computes such curves automatically and visualizes them in a web browser.

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“…The primary aim of this work was to develop a software tool to simplify and automate the identification and viewing of geometric loci in the plane. Loci problems are considered difficult in mathematical and graphical subjects all over the world [27], and their visual information can be useful in learning and professional contexts [28]. The tool, which is intended for educational used, can be implemented in any type of commercially available CAD software.…”

Section: Introductionmentioning

confidence: 99%

Computer-Aided Design: Development of a Software Tool for Solving Loci Problems

Hernández-Díaz

Hernández-Abad

et al. 2022

Symmetry

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In this work, we developed a software tool for the simplified, automated definition and viewing of loci in the plane, an essential task in the design, engineering and architectural fields. The process was started by identifying the most salient geometric loci in the engineering domain (i.e., tangents). A geometric approach was followed to deal with curves from the relative positions of two circles or a circle and a point. The algorithms used can be easily implemented in commercially available CAD software, which testifies to the usefulness and timeliness of the proposed tool. The tool successfully solved all target cases and was implemented as a function with the commercial software Adobe Authorware v.7.0.2.

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Achievements and Challenges in Automatic Locus and Envelope Animations in Dynamic Geometry

Abstract: A survey on the speed of real-time animation of loci and envelopes in the dynamic geometry software GeoGebra is presented.

Cited by 11 publications

References 8 publications

Acceptance of the GeoGebra Application in Learning Circle Theorems

Acceptance of the GeoGebra Application in Learning Circle Theorems

Automated Study of a Regular Trifolium

Computer-Aided Design: Development of a Software Tool for Solving Loci Problems

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