The first word of this item is "imagine". This instruction has the potential to signal a journey through a world of geometry that might leave you spellbound. On the other hand, it could be the start of a roller-coaster ride through three dimensions that will tax both your imagination, and your powers of visualisation. It is likely that you will…

Art uses mathematics in many ways. The author's teaching and involvement with mathematics and art in the Bridges Conference connecting the two have convinced him more and more that concepts for understanding mathematics can be achieved by the use of art. The author states that one reason he believes in teaching mathematics through art is that it…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

This article "opens up" the study of the relationship between quadrilaterals and circles to two sets of quadrilaterals--those that can be drawn either inside (cyclic) or outside (tangential) a circle (or both). Of course, "all" triangles are both cyclic and tangential. Or, to use the traditional Euclidean language for triangles, a unique…