Math 5530 - Topics in Non-Euclidean Geometry
Dr. Sarah J. Greenwald

Where to Get Help

  • Office Hours I am always happy to in office hours.
  • Check the main web page often for homework and for access to the other class pages.
  • ASULearn is the easiest way to ask a math question outside of class and office hours. You are responsible for reading all posts from me. I prefer that you use office hours since it is easier to discuss material in person, but if you can not make them, then it is a great alternative. I usually check it every day including the weekends.

    Required Resources

  • Experiencing Geometry: Euclidean and Non-Euclidean with History (3rd Edition) by David Henderson and Daina Taimina. Prentice Hall, August 2004. ISBN: 0131437488
  • manipulatives required to complete projects

    Course Goals and Objectives

    In what ways do the spaces we see in everyday life satisfy (and do not satisfy) the geometric laws and axioms of Euclidean geometry that we learn and teach in middle grades and high school classrooms? In this course we will explore spaces such as a tree trunk, ice cream cone, basketball, donut, coral reefs, Yoda from Star Wars, the world of taxi-cab drivers, Pac-Man's game, artistic works, and our universe via hands-on activities, computer explorations, theory, computations, axioms, applications, historical perspectives and pedagogical discussions. In this context we will understand Euclidean geometry at a much deeper level. In the final project, each student will develop a related lesson plan, notes for the teacher and solutions. Pre-requisite: Undergraduate calculus sequence with analytic geometry or permission of the instructor


  • Participation in Classroom Activities 25% You are expected to contribute to discussions in a meaningful way and actively engage the material. You must be prepared for each class and check the main web page regularly for hw. Attendance is required. These kinds of baseline activities will result in a participation grade of 16/20. Other activities can increase or decrease this grade. Utilizing office hours and ASULearn, asking and answering thought provoking questions, coming up with creative ways of thinking about the material, and explaining the material to others are some examples of positive participation that will increase your grade. On the other hand, performing activities that detract from the professional classroom environment or distract Dr. Sarah (who is very easily distracted) will result in a lowered participation grade. Many activities and class discussions are designed to be completed during class. Thus, attendance is required at ALL classes, and will form a portion of your grade. Missing more than the equivalent of 2 weeks during the semester (2 class days) will result in an automatic F in the course. Save your absences for emergencies. If the university is open and you miss a class, then that counts as an absence. If you must be late to a class, or must leave early, then do still attend.
  • Graded Homework 50% Work will not be accepted without explanation and must also be turned in on or before the due date. May occur during the last week of classes. If there is some reason you must miss a class, then obtain the assignment from the web pages. The lowest project will be dropped - save this for emergencies. Every other project will be equally weighted regardless of the total number of points. If all of your projects are turned in on time AND you have received at least a grade of 75% for all work, then you will receive an on-time credit of +1 added on to your final average. No lates allowed*.
  • Final Project 25% No make-ups allowed* In the final project, each student will develop a related lesson plan, notes for the teacher and solutions, and related references.

    *Work may occur during the last week of classes. Accommodations in the determination of your final grade will be made for extenuating circumstances that are documented to prevent you from completing work early/on time. In addition, Appalachian State University is committed to making reasonable accommodations for individuals with documented qualifying disabilities in accordance with the Americans with Disabilities Act of 1990, and Section 504 of the Rehabilitation Act of 1973. Those seeking accommodations based on a substantially limiting disability must contact and register with The Office of Disability Services (ODS) at or 828-262-3056. Once registration is complete, individuals will meet with ODS staff to discuss eligibility and appropriate accommodations. The grading scale is the same as the one in ASULearn grades: A ≥93; 90≤ A- < 93; 87 ≤ B+ <90...

    Other Policies and Methodology

    You are responsible for all material covered and all announcements and assignments made at each class, whether you are present or not. You are also responsible for announcements made on the web pages, so check them often.

    Asking questions, and explaining things to others, in or out of class, is one of the best ways to improve your understanding of the material. This course is to be an environment in which everyone feels comfortable asking questions, making mistakes, offering good guesses and ideas, and is respectful to one another. Turn in projects or prepare to present problems even if it they are not complete, even if only to say, "I do not understand such and such" or "I am stuck here." Be as specific as possible. When writing up work, be sure to give acknowledgment where it is due. Submitting someone else's work as your own (PLAGIARISM) is a serious violation of the University's Academic Integrity Code.

    In this course, you will be challenged with problems that you have never seen before. I do not expect you to be able to solve all the issues immediately. Instead, I want to see what you can do on your own. Out in the real world, this is important, since no matter what job you have, you will be expected to seek out information and answers to new topics you have not seen before. This may feel uncomfortable and frustrating. I understand this and want to help you through the process. It helps to remember that there are no mathematical dead-ends! Each time we get stuck, it teaches us something about the problem we are working on, and leads us to a deeper understanding of the mathematics.

    In the real world though, you are not expected to face your work alone. In this class, you are also not expected to face your work alone. I am always happy to help you in class, during office hours (or by appointment), or on ASULearn, and will try to give you hints and direction. At times though, to encourage the exploration process, I may direct you to rethink a problem and to come back to discuss it with me again afterwards. This occurs when I believe that the struggle to understand is imperative for your deep understanding of the material.