There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

Several times a week I walk by a metal chair that is fastened to a flat concrete slab at an outdoor bus stop here in Boulder. One day I noticed on the concrete a nice shadow image of the woven metal seat of the chair (Fig. 1). The seat and back of the chair are formed from 3.8-cm wide strips of metal spaced 3.8 cm apart. The seat is about 39 cm…

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Shows that the experiment of the ancient Greek mathematician and geographer, Eratosthenes, can be replicated and used to teach geographic concepts. Eratosthenes calculated the most accurate ancient measurement of earth based on fundamental mathematics concepts and earth-sun relations. Includes instructions, illustrations, graphs, and historical…

The first document in this set is a final report titled "Preparation for the Mathematics GED Test: A Computer Based Program," which describes a project to develop a General Educational Development (GED) mathematics preparation program for the adult learner at the 9-12 grade level. The other two documents are a teacher's guide and a…

This collection of activities demonstrates how the study of elementary mathematics can be extended beyond the school and involve teachers and students in investigative, problem-based experiences. The activities include topics in geometry, concept of number, algebra, measurement, graphing, statistics, and probability, and are organized into five…