Modern Geometries Syllabus Fall 2008

Instructor: Ron Smith
Office: 321 Zimmermann
Phone: Office: 784-5283; Home 784-6473

Office hours:

MWF 1-2:30 and TTh 9:30-12. For a 20 minute appointment, just sign up on the sheet outside my office door or call me. You do not need to sign up in advance, but if you will please sign when you come, the time will be reserved for you. Also, if someone is in the office and you are signed up, please make your presence known!


The required text is A Course in Modern Geometries, 2nd ed., by Judith R. Cederburg.


This course is a survey course in modern geometries, intended for students who have already had high school geometry or informal geometry. We will introduce finite, Euclidean, and non-Euclidean geometries, axiomatic systems in general, affine and projective geometries as invariants under transformation groups, and fractals.


The mathematical objectives of the course are to . . .
  1. Give an overview of the variety of modern geometries.
  2. Demonstrate the deductive nature of axiomatic systems.
  3. Acquaint students with the evolving notion of geometry.
  4. Introduce the students to reasoning with abstract objects.

Expectations for the student:

A modern geometry student will...
  1. Schedule at least 1 to 2 hours outside of class each day for studying geometry.
  2. Read each section carefully and write each proof with paper and pencil, endeavoring to fill in any missing steps.
  3. Look at problems besides those assigned to discover why the author asked the question.
  4. Prepare homework to hand in before class starts, including putting the name, class, homework number, and date on the outside.
  5. Come to class on time every day and stay the entire period,
  6. Have paper and pencil out on the desk at the beginning of class ready to work.
  7. Sit beside a partner with whom you will discuss geometry during class.
  8. Turn off electronic communication during class.
  9. Rest and eat before or after, but not during, class.
  10. Check all homework answers with the book and others, but write them up without copying.

Expectations of the Professor:

I will do my best to ...
  1. Start and end class on time, or within 3 minutes of the scheduled time.
  2. Be prepared for class every day.
  3. Grade and return homework and exams within 2 class days.
  4. Treat every student with respect.
  5. Learn each student's name.
  6. Answer every question in a respectful, truthful manner.
  7. Post homework assignments with clear due dates.
  8. Be available in my office during office hours, and give priority to anyone signed up.
  9. Grade all exams myself, completely, equitably, and clearly. Daily homework may be graded by an assistant. Not every homework problem turned in will be graded.
  10. Make every minute of every class a learning experience.


You will need 87.5% for an A, 75% for a B, 62.5% for a C, and 50% for a D. Grades will be based on attendance, homework, and exams. The points from all classwork, homework, and exams will be added. Your final grade is the percentage of the total possible.


If I bring food to the classroom, I will bring enough for everyone. I expect the same courtesy from students. Please do not eat personal snacks/meals in the classroom.


Cell phones, pagers, or other electronic devices intended to facilitate communication between students are not be used during lectures or exams.


Incompletes for the course require signing a contract for making up work, and must be initiated by the student.

Academic Integrity:

Honesty is a prerequisite for being a competent person. If you copy solutions to problems from any source, you are required to acknowledge the source. This includes copying from friends or old homework/test files. Working together for inspiration and asking for hints is allowed on everything but exams. However, writeups must be your own. For more on this subject, see the college policy printed in the handbook.


Any student who, because of a disabling condition, may require special arrangements in order to meet course requirements should contact the instructor as soon as possible to make necessary accommodations.

Tentative Course Outline

19/3/08Geometry Timeline
29/5/08Axiomatic Systems
49/10/08Proof Checklist
59/12/08Finite Geometry/Affine Plane Proofs
69/15/08Desargue's Configuration Axioms
79/17/08Desargue's Configuration Proofs
89/19/08Euclidean Geometry Propositions 1-30
99/22/085th Postulate
109/24/08Pythagorean Theorem per Euclid
119/26/08Star Geometry
1310/1/08Exam 1: Finite and Euclidean Geometries
1410/3/082.2 What did Euclid miss?
1510/6/082.3 Hyperbolic Geometry Intro
1610/8/082.3 Hyperbolic Geometry Continued
1710/10/082.4 Sensed Parallels
1810/13/082.5 Asymptotic Triangles
1910/15/082.6 Saccheri Quadrilaterals
2010/17/082.6 Continued
2110/22/082.7 Area of Triangles
2210/24/082.8 Ultraparallels
2310/27/082.9 Elliptic Geometry
2410/29/08Consistency of Formal Systems
2611/3/08Exam 2 Non Euclidean Geometries
2711/5/08Review of Matrix Multiplication
2811/7/083.1-2 Line and Point Reflections
2911/10/083.3 Rotations and Finite Symmetry Groups
3011/12/083.4 Translations and Frieze Pattern S. G.'s
3111/14/083.5 Analytic Model of Euclidean Plane
3211/17/083.6 Transformations of the Euclidean Plane
3311/19/083.7 Isometries
3411/21/083.8 Direct Isometries
3511/24/083.9 Indirect Isometries
3612/1/085.1 Chaotic Background
3712/3/085.2 New Geometric Language
3812/5/085.3 Fractal Dimension
3912/8/085.4 Iterated Function systems
4012/10/085.5 What is a fractal?
12/16/0810:00 Final Exam

Guidelines for Written Papers.

  1. Be neat!
  2. Fold papers together lengthwise to hand them in. Do not staple or tear, etc. The blank side of the paper is to be out. (See illustration below.)
  3. On the outside at the top, provide the following information as shown in the illustration.
    1. Name
    2. Class (Modern Geometries)
    3. Homework Number
    4. Date that you turn it in
  4. Clearly mark the section and number of each problem from the book.
  5. Include enough information on each problem so that the reader will know, without refering to the book, (a) what the book asked for, and (b) your response.
  6. Respect the equal sign "=". Use this sign only when you mean that the expression on one side can be substituted into any statement containing the expression on the other side without changing the truth value of the statement.
  7. Avoid "Type" errors. Use the equal sign "=" to connect two expressions only when they stand for the same type of expression, e.g. two numbers, two functions, or two sets. Use implies "=>" to connect two statements when the truth of the first guarantees the truth of the second. Sometimes, you will need to use an explanatory phrase such as "Therefore", "Now we can see", or "From equations (1) and (2)... in order to express the relationship between two statements.
  8. Write using complete sentences whenever possible.

Last Update: September 1, 2008
Ronald K. Smith
Graceland University
Lamoni, IA 50140