Presents mathematical games that involve a problem-solving matrix, multicolored cubes, and three-dimensional dominoes. The work of Alexander MacMahon is highlighted. (MA)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

The rational plane, consisting of the points in the Cartesian plane having two rational coordinates, is a model in which certain properties do not hold. Nine theorems are discussed. (MNS)

Methods of constructing polyhedra models are described. (DT)

This article provides a manipulative demonstration of the relationship between the squares on the sides of a right triangle. Materials are listed and directions are given for the student. Illustrations are included. (Author/MA)

An example of how geometry serves as a model in the real world is outlined, with suggestions on how it might be used at the high school level. (MNS)

Deciding, with outline maps, what highway exits to use to reach various towns most speedily is the problem presented. The simulation is geometric, focusing on loci. (MNS)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)

A method is described for representing quadratic functions by three-dimensional wire models. This enables one to form a simple geometric concept of the location of imaginary zeros. (MNS)

This exercise in mathematical modelling requires understanding of geometric progressions, inequalities, and absolutes. It presents a problem on credit creation in the banking system. (MNS)

Presents the theory of primary and secondary rainbow formation utilizing simple optics and geometric concepts. Describes an appropriate, waterless classroom demonstration and includes the relevant mathematical formulas and models. (JJK)

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invites students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MKR)

Presents two proofs that only five regular polyhedra exist. The first is a geometric proof, and the second is based on graph theory, using the relationship between the vertices, edges, and regions of the graph model. (MDH)

Several activities consistent with the error analysis method of teaching measurement are described. These activities illustrate the method which is then discussed in some detail. (SD)