Non-Euclidean Geometry
(MATH 6118-090, Spring 2006)

The Greeks believed that only the truth suits divine matters, not error or approximation, and the divine character of some matter made them more demanding in regard to accuracy. (We do exactly the opposite, being deformed by customs and propaganda.) It was because they saw a divine revelation in geometry that they invented rigorous demonstration.

(Simone Weil: Gravity and Grace)


Instructor: Gábor Hetyei
Office: Fretwell 335F, Phone: 704-867-2543, E-mail: ghetyei@uncc.edu
Office hours: MF 2:00-3:00 pm, W 3:00-4:00 pm, or by appointment.
Text: Non-Euclidean Geometry and a Little on How We Got There, lecture notes by David C. Royster. (Gray's Bookstore will prepare the copies for us.)
Prerequisite: Consent of the department.
Topics:
  • the origins of geometry
  • Euclidean geometry and constructions
  • transformation geometry
  • other geometries
  • the Poincaré disk model
  • hypercycles and horocycles
  • hyperbolic trigonometry and analytic hyperbolic geometry
We will try to cover all chapters of Prof. Royster's notes.
Test dates:
Midterm: Wednesday March 1, 5:00-7:50 pm.
Final Exam: Wednesday, May 10, 2005, 7:00 pm - 10:00 pm.
(Double-check in the UNCC Exam schedule !)
The final exam will be cumulative, consisting of two parts. The first part will be mandatory, covering only material taught after the midterm. The second half will contain questions reviewing the material taught before the midterm. This part will be optional, if left unanswered, I will substitute your midterm score.
Homework: Homework will be assigned every week, some to be turned in in writing, some will be presented by a randomly selected student in class. Since we meet only once per week, you should be planning on attending all lectures. If you are unable to come to a class, you have to work out in writing and turn in all homework assigned for oral presentation on that day. I will make an effort to regularly post the homework on the webpage
http://www.math.uncc.edu/~ghetyei/courses/6118/hw.html.
In case of discrepancy, what I said in class is "official".
Evaluation: Grades will be based on: 34% for the homework, 33% for the midterm, and 33% for the final (22% for the mandatory part, 11% for the optional part).
Class meeting: W 5:00-7:50 pm in Denny 217.
Homepage: http://www.math.uncc.edu/~ghetyei/courses/6118/index.html