Math-551, Euclidean and Non-Euclidean Geometries
Fall 2022
T,Th 9:30am-10:45pm, PH-381
Instructor: Richard Rimanyi
CP-429 (there is no phone in my office)
rimanyi@email.unc.edu
Course website: sakai
Prerequisite: Math 381.
Office Hours: Tu, Th 1:25, or by appointment, on Zoom 316 501 1964. Office hours
are intended to help you get unstuck — not started — on homework problems. Good
office hours questions tend to take the form “I understand the problem, I know the
definitions. I tried X, but it doesn’t seem to work because of Y ; what can I do?”
Communication with the instructor and classmates: All class related
communication, math or logistics, or anything else, must be on Piazza:
piazza.com/unc/fall2022/math551 .
Anonymous posting and private messages are enabled. I encourage mathematical
questions to be made open to all.
Text: we will follow this book:
https://rimanyi.web.unc.edu/wp-content/uploads/sites/9870/2021/12/
RR_Geometry.pdf . As an extra resource or for more exercises, some students find
Elementary Geometry, by I. Agricola,
T. Friedrich useful; it is available online through UNC library.
Final (according to UNC exam schedule): Tuesday, December 6, 8-11am.
Goals. In this course we will explore Euclidean geometry, spherical geometry, and
hyperbolic geometry. We will study incidence and metric properties of each of these
geometries. The philosophical aspects of the existence of multiple geometries will be
discussed.
About the course. I will lecture on the key points and difficult concepts, but you
will need to read the lecture notes for more details and review your class notes
regularly. Questions in class are encouraged.
Homework: Weekly homework will be assigned on sakai. Your score on each
problem will be based upon correctness and the quality of your presentation. No late
HW will be graded.
Group study is encouraged. Collaboration on homework, or consulting a tutor or
MHC is permitted. These rights, though, come with two responsibilities:
1. Write up your final solution independently from your collaborators.
Copied work is unacceptable.
2. Acknowledge all collaborators and tutors by listing their names at the
start of your solution.
Failure to shoulder these responsibilities constitutes an Honor Principle
violation and will be dealt with accordingly.
Midterms: The tentative dates of the two midterms are September 29, November 3.
The exact dates will be announced in class, at least a week ahead. There will be no
make-up midterms.
Grades will be based on a total of 500 points.
Homework 100
Midterms (2) 200
Final 200
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Total 500
I expect that 60% would suffice for a D, 70% for a C, 80% for a B, and 90% for an A.
No electronic devices are allowed in class.
It is expected that each student will conduct him or herself within the guidelines of
the Honor System. All academic work should be done with the complete honesty
and integrity that this University demands. All suspected Honor Code violations will
be reported to the Student Attorney General.
Disclaimer. The instructor reserves the right to make changes to the syllabus,
including due dates, test dates and grading scheme. All changes will be announced
in class or on Sakai.