This course provides students with the opportunity to broaden and deepen their understanding of Euclidean Geometry usually encountered in a high school geometry course. The course extends the geometric experience to non-Euclidean topics and serves to unify the study of geometry as the result of a system of axioms. Prerequisite: Grade of C or higher in MATH 222.
Prerequisite(s) / Corequisite(s):
Grade of C or higher in MATH 222.
Course Rotation for Day Program:
Offered odd Spring.
Most current editions of the following:
By Kay (Addison Wesley/Longman) Recommended
Foundations of Geometry
By Venema (Pearson) Recommended
To learn about the axiomatic nature of geometry.
To read, write, and critique geometric proofs.
To explore the similarities and differences between Euclidean and Non-Euclidean geometry
To use technology as an integral part of the process of formulation, solution and communication of geometric ideas.
Determine whether a set of axioms is consistent and independent.
Solve problems and complete proofs involving the axioms for points, lines, lanes and angles in 3-dimensional space.
Solve problems and complete proofs involving triangles, quadrilaterals and circles based on triangle congruencies.
Adapt the Parallel Postulate for Euclidean Geometry to develop the basic concepts of classical geometry, including concepts related to rectangles, regular polygons and circles.
Solve problems and complete proofs involving transformations (reflections, rotations and translations).
Describe the development of non-Euclidean geometry.
Perform various standard constructions by classical compass and straight edge and via technology.
Outline the surprising consequences of replacing Euclid’s parallel axiom with axioms that contradict it.
Axioms for Plane Geometry
Introduction to Hyperbolic Geometry
Introduction to Elliptic Geometry (Spherical Geometry)
Recommended maximum class size for this course: 20
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical
outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.