Students are introduced to the basic properties of axiomatic systems and investigate different axiomatic approaches to Euclidean geometry. Students gain an historical perspective of plane geometry by reviewing high school geometry, by proving more advanced results of Euclidean geometry (e.g., Ceva's theorem) and by exploring basic concepts of non-Euclidean and projective geometry as time permits. Students study transformational approaches to plane geometry, including the classification of motions and applications to symmetry patterns. Students may use Geometer's Sketchpad software to explore and discover geometric relationships (e.g., the altitudes of a triangle are concurrent). The course provides an overview of geometry suitable for mathematics majors who plan to teach in secondary school.
Evaluation of Students
Instructors typically use a combination of frequent, graded homework assignments (including Geometer's Sketchpad activities), quizzes, midterm exams and a final exam to evaluate students.
The following timeline is approximate.
|Number of Weeks
|Introduction to Axiomatic Systems
|Other Topics (as time permits, chosen from non-Euclidean and projective geometry)
Textbooks & Software
College Geometry: A Discovery Approach, (2nd edition), by David C. Kay. Methods of Geometry, 2nd edition, by J. James T. Smith. Geometer's Sketchpad software is installed in the Mathematics Department Computer Lab (TH 404). Students may also purchase Geometer's Sketchpad from Key Curriculum Press.
Submitted by: Bob Macucci
Date: May 28, 2003