Euclidean and non-Euclidean Geometry
M470, Spring 2006
Lecture: MWF 3:10-4:00, Engineering E203 (code 339335).
Course description: The meaning of the word "geometry" comes from Greek "to measure earth." It explains how the study of geometry started in ancient civilizations for practical purposes. For example, in Egypt the frequent flooding of the Nile made it necessary for people to have surveying techniques to make approximate measurements. Around 500 BC, Greek philosophers developed a new way of thinking, characterized by exactness, abstraction, and deductive reasoning. In some sense, the scientific method originates with their ideas. Euclid's book on this topic, "The Elements," is one of the oldest non-religious books still studied today. In simple terms, Euclidean geometry is about the relationships between points, lines, and circles on flat surfaces. To measure objects on a positively curved surface like a sphere, important modifications need to be made. Think about this the next time you get in an airplane! Many scientists now think that the universe is not flat and that its curvature may be negative. For these reasons, non-Euclidean geometry (spherical, hyperbolic, projective) is now an important topic to study.
Prerequisite: M229 and M261 or equivalent experience.
1) J. Stillwell, The Four Pillars of Geometry, Springer, ISBN 0-387-25530-3
2) Course Notes: See WebCT.
The course grades will be computed as follows:
30% homework; 20% midterm 1; 20% midterm 2; 30% final. Borderline grades will be decided on the basis of class participation.
Homework: Due every Friday.
Homework is the most important part of this class.
Doing homework problems is crucial for doing well in this class.
The process of doing homework will help you solve unfamiliar problems on the tests.
The homework problems will help you develop skills in
visualization, analytic calculation, and logical reasoning.
The grader will only grade homework which is neat, legible, and stapled.
I encourage you to brainstorm the problems in groups and write up your
Detailed information on homework
Extra credit project: Due 4/26. There are many amazing topics in geometry which we will not have time to cover fully. Each person has the opportunity to pick one of these and prepare a 2 page handout to share with the class. Some people will be chosen to give a 5 minute presentation on the project. This gives everyone a chance to learn one topic fully and to develop skill at presenting information. In addition, we'll see a snapshot of some fantastic topics.
There will be two midterms in class on Friday 2/24 and Friday 4/21.
There will be a final examination Thursday 5/11, 7-9 am in E203.
There are no makeups for missed exams, regardless of the reason for absence. You must take the final examination at this time scheduled by the university; no final exams will be given earlier. Examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.
Help: Help is always available if you have trouble with homework or lecture material. If your classmates can't answer your question, come ask me! Office hours are Wed 4-5, Thurs 10-11, or by appointment, in Weber 221.