In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

Geometry processing holds a foundational position within the realm of computer graphics, with advancements in this field regularly published at SIGGRAPH annually. The journey from writing the paper to implementing the algorithms is a meticulous and error-prone process, demanding significant dedication and attention to detail. Authors frequently…

Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

This article investigates the knowledge arising in mathematics teachers' planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the…

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

Background: Teachers must have the skills to find, select, design and use technology-based mathematical activities that focus on high-level cognitive demands--supporting student reasoning. However, they experience various difficulties in creating, planning and making decisions about how and when to utilize technological affordances. Objectives:…

Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…

The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

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…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…