ARCHIVE PAGE

This page is not updated any more.

Non-Euclidean Geometry
(MATH 6118-001, Spring 2018)

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: 704-687-1045, E-mail: ghetyei@uncc.edu
Office hours: Mondays and Wednesdays 5:00-6:00 pm and Tuesdays 4:15-4:55 pm, or by appointment (eventual changes will be announced in class). Tuesday office hours were changed on Friday, January 12, 2018
Text: Roads to Geometry, 3d Edition by Edward C. Wallace and Stephen F. West.
Prerequisite: Consent of the department.
Topics:
  1. Axiomatic Systems: Historical Background (only important highlights)/ Axiomatic Systems and Their Properties (read at home)/ (skip Finite Geometries) / Axioms for Incidence Geometry
  2. Axiom Sets For Geometry: Euclid's Geometry and Euclid's Elements / Modern Euclidean Geometry / Hilbert's Axioms for Euclidean Geometry / Birkhoff's Axioms for Euclidean Geometry / The SMSG Postulates for Euclidean Geometry / Non-Euclidean Geometry
  3. Neutral Geometry: Preliminary Notions / Congruence Conditions / The Place of Parallels / The Saccheri-Lengendre Theorem / The Search for a Rectangle
  4. Euclidean Geometry of the Plane: The Parallel Postulate and Some Implications / Congruence and Area / Similarity / Some Euclidean Results Concerning Circles / Some Euclidean Results Concerning Triangles / More Euclidean Results Concerning Triangles / The Nine-Point Circle / Euclidean Constructions / (skip Laboratory Activities Using Dynamic Geometry Software)
  5. Analytical and Transformational Geometry: We will cover Inversion, the rest of the chapter will be covered if we have time left and there is interest.
  6. Non-Euclidean Geometries: A Return to Neutral Geometry: The Angle of Parallelism / The Hyperbolic Parallel Postulate / Hyperbolic Results Concerning Polygons / Area in Hyperbolic Geometry / Showing Consistency: A Model for Hyperbolic Geometry / Classifying Theorems / Elliptic Geometry: A Geometry with No Parallels? / Geometry in the Real World / (skip Laboratory Activities Using Dynamic Geometry Software)
We will try to cover as much of the book as we can, with a focus on the above indicated topics.
Test dates:
Midterm: Tuesday February 27, 5:00-7:45 pm.
Final Exam: Tuesday, May 8, 5:00-7:30 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://math2.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: Tuesdays 5:00 - 7:45 pm in Fretwell 405 The classroom location was changed on Friday, January 12, 2018
Homepage: http://math2.uncc.edu/~ghetyei/courses/6118/index.html