Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)

Finding areas on square grid and on isometric grid geoboards is explained, then the Pythagorean Theorem is investigated when regular n-gons and when similar figures are erected on the sides of a right triangle. (DT)

For students having had instruction in plane affine geometry and two-dimensional vector spaces. The author describes how the metric concepts of distance and orthogonality can be introduced to secondary school students by the use of conics. (JG)

Five solutions to the problems of constructing an equilateral triangle within any triangle and having the vertices on the sides of the given triangle are presented and a generalization is made. (CT)

A question posed by Euler is considered: How can polyhedra be classified so that the results is in some way analogous to the simple classification of polygons according to the number of their sides? (MK)

Worksheets and instructions are given for this activity whose objective is to develop the relationship between the lengths of the sides of a triangle and its classification by angle. (MP)

Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (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…

Before the 19th century the idea of more than three dimensions was exceptional. During the 19th century, however, geometry was revolutionized and new branches were developed. This revolution also created the idea of the possibility of a n-dimensional geometry or space; flatland, i.e. n = 2, was a consequence of this new thinking. In 1884 the…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact…