Developing a finite Geometry: A Math Club Approach

High School students who have had successful experience with elementary algebra, naive set theory, plane geometry, and mathematical systems form the audience for whom this paper was written. It is hoped, however, that others, too, will find it appropriate and enjoyable. It provides an example of a finite geometry; the axioms for a nine-point geometry are presented and used to prove ten theorems in a mathematically sound development. It illustrates the use of intuition (particularly sketches) in developing a rigorous proof. It strengthens the concept of mathematical system; to solve a complicated problem, the students in the story develop a mathematical system that describes the problem situation. Readers will undoubtedly discover other uses.