Provides examples of proofs of the Pythagorean result. These proofs fall into three categories: using ratios, using dissection, and using other forms of transformation. Shows that polygons of equal area are equidecomposable and that the approach taken (via squares) is a new approach. (JN)

The study and use of "Venn diagrams" can lead to many interesting problems of a geometric, topological, or combinatorial character. The general nature of these diagrams is discussed and two new results are formulated. (JN)

Shows how to construct a cube using Origami techniques. Also shows how, by identifying analogous features, to construct an octahedron. (JN)

Presents a sequence of activities which serve to unravel the mystery of pi. In addition, the activities give meaning to circle relationships that formerly have been, at best, rotely learned. (JN)

Discusses the derivation of Pick's theorem. However, this derivation is beyond the grasp of most high school students. Therefore, a sequence of simple exploratory activities is provided which will enable students to discover and apply Pick's theorem for finding the area of a polygon whose vertices are lattice points. (JN)

Discussed for use with learning disabled children are the geometric materials and teaching methods developed by M. Montessori. (DB)

The fundamental role of the theorems of Pappus and Desargues in the construction of nomograms is explained. (DT)

An example of mathematizing a situation and mathematical model-building by means of using a finite geometry is presented. (DT)

The geometry curriculum at the elementary school level is discussed. Details of five different units on geometry, each stressing space orientation, are given. (DT)

Using an incorrect conjecture as a learning activity in mathematics is discussed. The example used is from transformation geometry. (DT)

Achievement levels of geometry classes were compared following units of instruction employing analytic, synthetic, and combination strategies. For above-average and below-average achievement groups, instruction with different strategies was found to yield differences in MANOVA - identified achievement composite scores. (Author/DT)

The aim of this research is to advance understanding of how mathematical knowledge functions in the proving in geometry. We focus on the rules whose mobilization is due rather to the mathematical knowledge at stake than to the proof. We observed students who are asked to solve construction problem and proving problem. The problems require to…

This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…

This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…