The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

Solid polyominoes are formed by gluing cubes together so that the two faces of adjacent cubes are wholly in contact. Tessellations of a three-dimensional space with solid pentominoes are discussed and illustrated. (MP)

Presents an activity to identify some square-differences on the multiplication table. Discusses these properties using the Pythagorean triangle. (ASK)

Offers an alternative instructional method of constructing cubes based on the use of linking smaller cubes to form triangles. Offers learners insight into algebra by clearly exposing the underlying structure of the problem-solving process. (ASK)

This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…

Many educators believe that solid modeling software has made teaching two- and three-dimensional visualization skills obsolete. They claim that the visual tools built into the solid modeling software serve as a replacement for the CAD operator's personal visualization skills. They also claim that because solid modeling software can produce…

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)