Two well-known theorems from geometry are shown to be essentially the same using the principle of duality of lines and points. (MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

A detailed proof is given of a theorem that characterizes the vertex sequence of any convex polyhedron and establishes the existence of only 13 Archimedean solids. (MP)

A brief overview is presented of the use of soap bubbles to solve minimal problems. A new class of problems that can be solved with soap film models is presented. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

Some unconventional word problems containing excessive, inconsistent, or inadequate data and their possible limitations and benefits in a mathematics classroom are discussed. (JT)

A different method for solving quadratic equations and inequalities is proposed. The method is applicable to solving quadratics over the set of real numbers as well as the complex field. (JT)

A unit analysis approach, advocated by science teachers, teaching students to solve proportions, is described. (JT)

Performance objectives for precalculus mathematics are listed after a look at the content of current calculus courses. (JT)

The ideas presented include a number line activity for addition and subtraction of integers, a game involving polynomials that encourages mathematical guesswork and deduction, and an introductory story for parabolas. (JT)

An activity that offers computational practice, pattern recognition, and the formulation of generalizations is described. (JT)

A set of rules is given for developing pairs of numbers which can be plotted on a graph, to provide practice not only with graphing but also with computation. (JT)

The origin of the magic square, its numerical concepts, and some procedures for its construction are discussed. (JT)

A combination of trigonometry and algebra is used to focus on the concept of congruent triangles. (JT)

The target point for the cue ball in a simplified game of billiards is computed through the use of line reflections and computations with complex numbers. (JT)