In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the…

The present paper describes a dynamic investigation of polygons obtained by reflecting an arbitrary point located inside or outside a given polygon through the midpoints of its sides. The activity was based on hypothesizing on the shape of the reflection polygon that would be obtained, testing the hypotheses using dynamic software, and finding a…

This paper aims to clarify how the use of the GeoGebra dynamic geometry program helps students understand the relationships between different representations of a linear function and develop the ability to plot a linear function. The study was based on a quasi-experimental design. In control classes, the topic of functions was presented without…

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students' geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the…

Recent research in mathematics education shows that by exploring the properties of figures and making conjectures, especially through dynamic geometry software, students can better develop their understanding of concepts. Furthermore, comparing different geometric worlds and, within them, different representations enhances Euclidean knowledge. In…

This study investigates the use of GeoGebra, a Dynamic Geometry Software (DGS) for math learning in Virtual Reality (VR) using head-mounted displays. We conducted a study with n = 20 middle school students receiving a mathematics tutoring intervention over time in a VR environment. Using theories of embodied cognition and playful mathematics, this…

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was…

Learning geometry with conceptual understanding requires the implementation of appropriate methods that actively engage students and support them in becoming autonomous, critical thinkers, and self-directed learners. The purpose of the study was to investigate the effect of GeoGebra-supported learning on grade ten students' conceptual…

In this paper a class of regular surfaces, generated by rotation and twist of a rigid line segment, is considered. Firstly a complete description of those surfaces by means of local charts is obtained and then its orientability is characterized in terms of the number of half-twists, taking into account their direction (clockwise or…

The low knowledge and love of students for culture, plus based on preliminary analysis, it is known that geometry skills are relatively low. The a need for harmony between student and teacher learning styles to maximize student engagement and focus in the classroom. So this study aims to create a culture-based Geometry learning design that…

In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

We implemented GeoGebra software in Rwandan secondary schools to check its effectiveness during teaching and learning geometry concepts. The quasi-experimental design was used, and four schools were purposefully selected. Two schools were from Northern Province, while the other two were selected from Kigali city. A geometry-based test composed of…

Conjecture formulation is crucial to mathematics education. Therefore, this study aimed to evaluate challenges prospective mathematics teachers (PMTs) encounter when using GeoGebra to formulate geometrical conjecture. A qualitative case study was conducted with an exploratory strategy to provide a complete comprehension of the occurrence. Six…

Limited literature addresses how elementary preservice teachers (PSTs) can advance their thinking about hierarchical geometric relationships. Informed by a commognitive perspective, we investigated this phenomenon as a matter of discursive change, focusing on word use, visual mediators, and narratives. We report on a teaching experiment involving…

This study examined students' views on geometry teaching via three-dimensional dynamic geometry software Cabri 3D. Teaching designed with Cabri 3D for solids volume measurement was implemented for 16 students in the eighth grade from a public secondary school in Turkey. The data obtained from the interviews with the students about the teaching,…