Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…

There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

In this paper, difficulties of students in the case of computer-mediated teaching of geometry in a traditional classroom are considered within the framework of "transactional distance", a concept well known in distance education. The main interest of this paper is to record and describe in detail the different forms of…