A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they…

Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations. A range of classroom…

A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

The perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we…

Interesting conservation properties that exist in parallelograms are well known, such as: diagonal intersection, pairs of interior triangles that overlap each other, and other properties. This article presents a dynamic study of choosing any point inside and outside the parallelogram and connecting it with two of the vertices of the parallelogram.…

This thesis focuses on the challenge of characterizing multipartite entanglement. While the study of bipartite entanglement is well-documented in scientific literature, recognizing that entanglement can involve more than two parties--i.e. three or more parties---is crucial, as multipartite entanglement enables the completion of more complicated…

Throughout the years of the history of the development of mathematics, starting with the ancient mathematicians, new things were discovered from time to time, which made it a central component of the computerized world, which serves us in many fields, with the young "swimming" in it, and the adults asking: how could we live without it!…

Hands-on experiments with overturning some prisms (partially filled with water) lead students to a conjecture which can be confirmed by using a 3D geometry programme and reinterpreting the process of "overturning of a prism" in an appropriate way. But such confirmations are not a proof and particularly cannot answer the question…

Polyiamonds are the 'and so on' when unit-squares are replaced with unit-equilateral triangles. Polyiamonds are used to play the satisfying Blokus variant, Blokus Trigon, where the playing grid is also hexagonal, and the playing pieces are all the polyiamonds from mono- to hex. This article discusses the use of polyiamonds in puzzles.

In this work, we delve into geometric analysis, particularly examining the interplay between lower bounds on Ricci curvature and specific functionals. Our exploration begins with an investigation into the implications of Yamabe invariants for asymptotically Poincare-Einstein manifolds and their conformal boundaries under conditions of…

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

Certain terms in mathematics were created according to conventions that are not obvious to students who will use the term. When this is the case, investigating the choice of a name can reveal interesting and unforeseen connections among mathematical topics. In this study, we tasked prospective and practicing teachers to consider: What is geometric…

An interesting geometric conservation problem is presented. Here proof is presented in a 'proof without words' style, with the aim of developing the reader's visual proof ability. The study of the task and its expansion is accompanied by a dynamic sketch to highlight the conservation property.

Prior research suggests that creating art can reduce mental health symptoms, such as anxiety. It has also been proposed that creating art within the geometric shape of a circle may confer additional therapeutic benefits. However, it remains unclear whether creating art within a circle or creating art with no restrictions reduces anxiety in both…