Mathematics 635

MATH 635. Euclidean and Non-Euclidean Geometry

Prerequisite: Undergraduate Geometry course, or by instructor permission.

Three Credit Hours (3)

This course will introduce students to systems of postulates in a comparison of Euclidean and Non-Euclidean geometries.  Geometric structures of transformational, fractal, and projective geometry are examined together with a brief history of the development of axiomatic systems of geometry.

Detailed Description of Course

The development of Geometry as an axiomatic system starting with pre-epoch Greece, and following through to Non-Euclidean Geometries. The geometries examined will consist of Euclidean, Neutral, and Elliptic and Hyperbolic (non-Euclidean) geometries. Selected topics from the following geometries will be included: Absolute Geometry, Finite Geometries, and Taxicab Geometry. Projective geometry will be examined through perspective drawings. The comparison between concepts in Euclidian and Non-Euclidian Geometries will be treated through vertical articulation using hands-on exploratory, and student-centered activities.

Detailed Description of Conduct of Course

In addition to lecture, students will work collaboratively on assignments created to help students understand the mathematics introduced.  Calculators and mathematics software, such as Geometers Sketchpad, GeoGebra, Spherical Easel, Cinderella, and Excel will be used to present and work on the material presented in class. Students will also develop sketches using manipulatives such as Lenart Spheres, Magformers. A project will be presented by the students on a topic chosen by the instructor. The graduate students will have an additional graduate level cumulative final project designed to create instructional materials related to the course content that can be shared with others across the state and nation.

Goals and Objectives of the Course

Students will develop an understanding of and appreciation for axiomatic systems and their role in problem-solving in mathematics.  Students will examine the interconnections among the different types of geometry and the expansive nature of mathematical development.  They will build knowledge of the role of geometry in understanding the world and of how this understanding can be developed in their own classrooms.  They will extend their conceptions of geometry beyond plane figures and their properties.

Assessment Measures

Students will demonstrate content understanding through written (possibly oral) exams, written homework problems, collaborative work in class, and a project.   

Other Course Information



Review and Approval

May 2, 2016
November 2008