In mathematics, three integer numbers or triples have been shown to govern a specific geometrical balance between triangles and squares. The first to study triples were probably the Babylonians, followed by Pythagoras some 1500 years later (Friberg, 1981). This geometrical balance relates parent triples to child triples via the central square…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…

The international debate about experimental approaches to the teaching and learning mathematics is very current. While number theory lends itself naturally to such approaches, elementary geometry can also provide interesting starting points for creative work in class. This article shows how simple considerations about right triangles and the…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

In this article, the author argues that coordinate geometry and all its trappings should be banned from key stage 2 in English schools. To explain why he makes such a strong statement, he discusses geometry problems tackled by the Ancient Greeks, showing how meaningful problem solving can occur without the use of coordinates and the corresponding…

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and…

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

The converse of a familiar construction problem is explored, and a partial solution presented. The general problem is "Given a segment with length whose square is x, construct a segment with length 1." (SD)