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Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2019

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.

Descriptors: Geometry, Geometric Concepts, Secondary School Mathematics, High School Students

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2019

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°.

Descriptors: Mathematics Instruction, Teaching Methods, Manipulative Materials, Mathematical Concepts

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2018

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…

Descriptors: Teaching Methods, Validity, Mathematical Logic, High School Students

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2018

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.

Descriptors: Geometric Concepts, Geometry, Mathematical Models, Problem Solving

Wares, Arsalan; Elstak, Iwan – International Journal of Mathematical Education in Science and Technology, 2017

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…

Descriptors: Geometry, Art Activities, Mathematics Activities, Algebra

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2017

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

Descriptors: Mathematics Instruction, Geometric Concepts, Mathematical Logic, Validity

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2013

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…

Descriptors: Teaching Methods, Mathematics Instruction, Mathematical Concepts, Geometric Concepts

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2011

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…

Descriptors: Geometric Concepts, Geometry, Calculus, Mathematics Instruction

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2010

The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

Descriptors: Geometry, Mathematical Logic, Validity, Mathematics Instruction

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2008

This note describes two conjectures pertaining to repeated partitioning of an arbitrary triangle. The first conjecture turns out to be true, and hence gives rise to a new, more general, conjecture that is also addressed in this article. Both conjectures can be explored in a dynamic geometry environment. The proofs to the conjectures addressed in…

Descriptors: Geometric Concepts, Geometry, Mathematical Logic, Validity

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2004

Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students…

Descriptors: Mathematical Logic, Geometry, Computer Software, Teaching Methods

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2002

This note describes a large-scale modelling activity involving geometry that can be solved with the help of uni-variable calculus. More specifically, it introduces and proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given…

Descriptors: Calculus, Mathematics Instruction, Geometric Concepts, Mathematical Models