Describes how many of the geometrical and physical properties of the binary elastic collision of two particles can be represented by an isoceles trapezoid in the velocity space. (BB)

An activity is presented which involves making a stadia tube from a cardboard mailing tube and using it to measure horizontal and vertical distances using the properties of similar triangles. (MN)

The use of basis matrix methods to rotate axes is detailed. It is felt that persons who have need to rotate axes often will find that the matrix method saves considerable work. One drawback is that most students first learning to rotate axes will not yet have studied linear algebra. (MP)

Some ways of thinking and acting geometrically are described which are related to the approach used by ancient humans. The focus is on intuitive geometric imagery, an attempt to resurrect a way of describing possible viewpoints of geometry outside of those commonly accepted. (MP)

Activities designed to lead pupils through the process of using the basic measuring and drawing devices of geometry are presented and move to the discovery of several surprising generalizations about arbitrary triangles. (MP)

Describes an activity in which students observe a simple situation, explore conjectures, and generate conclusions from their exploration of the conjectures to develop the essential triangle-congruence theorems. Includes teacher's guide. (KHR)

Presents Heron's original geometric proof to his formula to calculate the area of a triangle. Attempts to improve on this proof by supplying a chain of reasoning that leads quickly from premises to the conclusion. (MDH)

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

What aspects of spatial relations influence speakers' choice of locative? This article presents a study of static spatial descriptions from 24 languages. The study reveals two kinds of spatial terms evident cross-linguistically: specific spatial terms and general spatial terms (GSTs). Whereas specific spatial terms--including English…

Using the film "Journey to the Centre of a Triangle" with a group of 15-year-old pupils, the author describes how they had done some work on constructions such as angle bisector and perpendicular bisector. The pupils were given A3 papers, rulers, compasses and pencils and they were asked to recreate their favourite scence from the film. The film…

This textbook commences with a brief sketch of the history of Elementary Geometry. The definitions throughout have been somewhat amplified, and several notes have been added which it is hoped may be found useful and suggestive. The subject of Ratio has been expanded; a few new propositions have been added; and there is a considerable collection of…

This textbook is designed to be used in a geometry course incorporating the writings of Euclid. The object of this edition now offered to the public, is not so much to give the writings of Euclid the form which they originally had, as that which may at present render them most useful. The author believes that the use of algebraic signs and…

This textbook covers the first six books of the elements of Euclid, the 11th and 12th books, and the book of Euclid's data. Elements of plane and spherical trigonometry are included.