Math 3610
Introduction to Geometry
Dr. Sarah J. Greenwald

Required Resources

  • Rental: The Geometric Viewpoint: A Survey of Geometries by Thomas Q. Sibley
  • Rental: Roads to Geometry by Edward C. Wallace and Stephen F. West
  • Rental: i-clicker
  • access to the software package Geometer's Sketchpad (GSP), which is available in some computer labs on campus. If you have time to work during the hours these are available, this suffices. Otherwise you'll purchase a copy---the student pricing is a 1-year license for $9.96 (a non-expiring license costs $70.02, if you prefer that) at
  • A more limited App, Sketchpad Explorer, is available for free on the iPhone, iPad, and iPod touch
  • printouts of your work, including your Sketchpad work
  • manipulatives required to complete projects

    Where to Get Help

  • Office Hours 326 Walker Hall, 262-2363. I am always happy to help you in office hours. Any changes, extra additions or cancellations are announced online when possible. Sometimes, if no one comes to office hours, I go down the hall to the mailroom, photocopy machine, or to talk to another professor. If I am not in my office during office hours, you should walk down the hall to look for me, and interrupt to tell me that you are there. You do not need to make an appointment to use office hours - just drop by! I am happy to answer your questions, go over material you are not feeling comfortable with, or help you work on homework or projects. If someone else is in my office hours, join us - we'll take turns for questions. I strongly prefer that you use office hours, but if you can't make them, message me on ASULearn Forums.
  • Check the main web page often for homework and for access to the other class pages.
  • ASULearn This is the easiest way to ask a mathematics 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 ASULearn is a great alternative. Do NOT email me (which gets buried in hundreds of messages each day) - message me instead as I usually check it every day including the weekends.

    Course Goals and Objectives

    A study of the development of Euclidean geometry through multiple perspectives, including synthetic and metric. Topics to be considered include parallelism, similarity, measurement, constructions, an axiomatic approach to polyhedra, and at least one non-Euclidean geometry. The course will focus on concept development and connections among mathematical perspectives. Prerequisites: MAT 1120 and either MAT 2110 or MAT 2510. (SPEAKING)

  • In order to foster concept development and connections among multiple perspectives, we will examine the foundations of geometry through the lenses of mathematical reasoning and proofs, manipulatives, dynamic geometry software, and the historical progression of geometry.
  • We will also develop problem solving and visualization skills and express geometric concepts in a variety of formats. Math 3610 has been designated as a speaking course. In order to satisfy the speaking designation, presentations will occur during the semester and during a final project, as well as informal opportunities for speaking that will occur regularly in small groups and whole class discussions.

    This is a mathematics content course, which means that it is designed stimulate your intellectual growth and mathematical developement. Many of you intend to be teachers so some of the mathematics covered in the course will be related in meaningful ways to materials that can be taken into the classroom (for example, various ways of teaching and learning geometry will be modeled).


  • Participation in Classroom Activities 10% You are expected to contribute to discussions and i-clicker questions in a meaningful way and actively engage the material in class and lab. You must be prepared for each class and check the main web page regularly to turn in hw. Attendance is required. These kinds of baseline activities will result in a participation grade of 7/10. Other activities can increase or decrease this grade. Utilizing office hours and ASULearn, asking and answering thought provoking questions, coming up with creative or fun 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. Cell phones must be set to vibrate or turned off and they are not allowed on tests. No texting during class. 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 participation grade. In addition, missing more than the equivalent of 4 weeks during the semester (8 class days of 1:15) will result in an automatic F in the course. Save your absences for emergencies.
  • Projects 35% 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. No lates allowed*.
  • Work Completion +1 If you have earned a passing grade of at least a grade of 60% for every project (including the dropped one), and you have turned in all the other homework by the due date, then you will receive +1 added on to your final average.
  • Exams 45% There are 2 tests over the course of the semester. You should view exams primarily as a learning experience. This means that exams are not only an opportunity for you to demonstrate your mastery of the material, but are also an opportunity for you to be challenged with new material in order for you to make new connections. No late tests allowed*. May occur the last week of classes.
  • Final Research and Review Presentation 10% during our assigned time in finals. Must participate to pass the class.

    * 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. The grading scale is: A ≥93; 90≤ A- < 93; 87 ≤ B+ <90...

    Also see the University-wide syllabus and policy statements which we adhere to.

    Other Policies and Methodology

    As per the University-wide Statement on Student Engagement with Courses you can expect to spend (on average) 2-3 hours outside of class for each hour in class. 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. Your other time outside of class should be spent reviewing course material, completing homework assignments and projects, reading solutions on ASULearn, or spending time in office hours.

    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.

    You should explore each problem and write out your thinking in a way that can be shared with others. Focus on your own ideas. 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, , which defines:

    Plagiarism includes, but is not limited to, borrowing, downloading, cutting and pasting, and paraphrasing without acknowledgement, including from online sources, or allowing an individual's academic work to be submitted as another's work.

    Use of interactive technology is allowed only when it is related to our class. Put cell phones away and set them to vibrate. Photos or video or audio recordings may not be taken in class without prior permission. Food and beverages are allowed as long as they aren't distracting, but e-cigs, chewing tobacco/spit cups and other products are not allowed.

    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.

    Tentative Course Calendar

    Date     WORK DUE at the beginning of class unless otherwise noted!
    6 May - Wed
  • Our assigned meeting time during finals week is Wed May 6 beginning at noon. You must participate in the Final Research and Review Presentation, which is a continuation of Project 4, to pass the class.
  • More on transformations
    23 Apr - Thur
  • Test 2 on Polyhedra, Metric Perspectives, Parallelism, and Non-Euclidean Geometry
  • 16 Apr - Thur
  • Project 6: Parallels and Connections
  • Parallels
    31 Mar - Tues
  • Project 5: Polyhedral and Metric Considerations
  • Metric Perspectives and Coordinate Geometry
    17 Mar - Tues
  • Project 4: Concept Development (Historical Timeline Presentations)
  • Concept Developement
    Area and Volume
    24 Feb - Tues
  • Test 1 on Axioms, Constructions, Measurement, and Similarity
  • Polyhedra
    12 Feb - Thur
  • Project 3: Similarity
  • Pythagorean Theorem and Extensions
    3 Feb - Tues
  • Project 2: Connections and an Overview of Course Topics (Sphere Presentations)
  • Similarity
    22 Jan - Thur
  • Project 1: Measurement and Constructions
  • Introduction to Axiomatic Systems and Geometric Constructions

    Instructor Bio

    I am a Professor of Mathematics and a Women's Studies core faculty member at Appalachian State University. I received my PhD from the University of Pennsylvania. My scholarship areas include Riemannian geometry of orbifolds (linear algebra is important here), popular culture as it pertains to mathematics, and women and minorities in mathematics. Recognition for my teaching includes a 2005 Mathematical Association of America Alder Award winner for distinguished teaching and the winner of the 2010 Appalachian State University Wayne D. Duncan Award for Excellence in Teaching in General Education. In 2010 I was also inducted into the Appalachian State University College of Arts and Sciences Academy of Outstanding Teachers and in 2011 I was named the College of Arts and Sciences Outstanding Teacher of the Year. I am the associate editor of the Association for Women in Mathematics Newsletter and a member of the editorial board of PRIMUS. Andrew Nestler and I co-created the educational website My interactive mathematics lecture has been distributed on approximately one million DVDs worldwide as a 25-minute DVD extra for the 20th Century Fox Futurama movie Bender's Big Score and it is listed as "Mind-bending." Jill Thomley and I co-edited the 3-volume Encyclopedia of Mathematics & Society, which was named a "Best Reference 2011" by Library Journal. I've spoken about the impacts of scientific popular culture representations on NPR's Science Friday and all over the country.

    I am married to the bassist Joel Landsberg. We both happen to be on IMDb: Joel and me. My Erdos Bacon number is 6-7 or infinity, depending on what/how you count. In my spare time I like to travel, hike and conduct genealogy research (I also enjoy popular culture, as you can probably tell from some of my scholarly interests). In addition to my own personal genealogy, I like to give back to the broader community. I am the project coordinator for sites like the Bialobrzegi ShtetLink and the Book of Remembrance of the Community of Bialobrzeg. These projects strive to research and preserve information about communities that were destroyed in World War II. My great-grandparents lived there (it was the Russian empire back then!) in the late 1800s. Some of what I really like about mathematics is also what I enjoy about genealogy - the sense of exploration, discovery and aha moments that come with lots of patience and effort.