The purpose of this note is to introduce two challenging problems in geometry that were inspired by some well-known problems in high school geometry. These problems can be explored in the dynamic geometry environments of computer construction programmes.

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus.

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

In this article, the author describes an occurrence of the golden ratio in the context of regular hexagons. The method described can be used to construct the golden ratio. This is one of many ways one can construct the golden ratio.

The purpose of this note is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of geometry and algebra.

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

The purpose of these notes is to provide examples of large-scale geometry problems that have the potential to promote "constructive struggling" in high-school geometry classrooms. These problems are suitable for being explored in a dynamic geometry environment. The notes also contain brief sketches of solutions to the two problems.

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

The purpose of this short paper is to describe a new proof of the Pythagorean Theorem that involves paper folding.

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important mathematical concepts in geometry like surface area. This article describes how an origami box can be folded from a rectangular sheet of paper, then it goes on to describe how its surface area can be determined in terms of the…

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…