Math 340. Geometry

Fall 2022


Proofs of Desargues and Pappus in the book "A survey of classical and modern geometries" by Baragar.

No class on Friday October 7.

The following Scientific American article written by Evelyn Lamb contains the diagram of president Garfield's proof of the Pythagorean theorem and a diagram from an ancient Chinese book (probably from 1 B.C.E) that actually proves the Pythagorean theorem in two ways.

This New Yorker article written by Steven Strogatz gives a very nice background (and explanation) on Einstein's proof of the Pythagorean theorem. Strogatz wrote a wonderful series of articles in the New York Times explaining math to a general audience. It is titled Elements of Math.

Self-Explaining Booklet, is a short file with tips that can help you read proofs better.

The homework assignments can be found below:
Homework Assignments

Course Description

Selected topics from affine, Euclidean, non-Euclidean, projective, and differential geometry. Prerequisite: Mathematics 230 or permission of the instructor. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.)
Student Learning Outcomes


The Four Pillars of Geometry by John Stillwell.

Topics we will cover

I will warn that there's a good chance of not covering all of these subjects as I think Euclidean geometry is the main topic to cover in this class and will spend extra time on it if I deem it necessary.


The course grade will be based on:
Homework 48%,
Class Participation 8%
Midterms 24% (12% each),
Final Exam 20%.


The course will have the following structure. There will be homework assignments on a roughly weekly basis. I will assign them usually on a Friday. On the Tuesday following the assignment, you can meet with me to ask for hints on problems you are stuck. I will only provide hints if I see evidence that you have worked at least 4 hours on the assignment. To figure this out, I will ask questions such as "What have you tried?" and perhaps ask you to show me your work so far. After this hint-day, you have three more days to complete the assignment and turn it in on Friday. You are allowed to work with others on the homework, but your homework should be your own. Furthermore, you will not be allowed to use the internet (other than things I post on this website) or other books as aids.
There will be 8 homework assignments. Each homework assignment will be worth 6% of your grade. Homework will not be accepted late.

There will be two midterms and one final exam. The three exams will be take-home exams and will have the same structure as the homework. You will get the assignment, have 3 days (or four) to work on it. Ask for hints on Tuesday and then turn it in on Friday. One big difference with homework assignments is that in exams you will be able to resubmit after feedback. Another difference with homework assignments is that on exams you will have to work entirely on your own (except for asking me questions) with the same restriction of NO INTERNET and no use of other books.

The (tentative) dates for the exams are
Class Participation

I expect you to come to every class, pay attention, and to ask questions when you have questions. Some classes will have in-class activities, when these occur, you should be working on the task at hand.

Accommodations Statement

If you are a student who needs an accommodation because of a disability or medical or psychological condition that limits your ability to fully participate in this course, please contact Kara Fifield (, Director of Disability Services, to document your disability with the College and with the professor of this course. Academic accommodations should be reasonable and not alter the fundamental nature of this course. Because it can take a week or more to arrange requested accommodations, you are encouraged to establish your semester accommodations as early in the semester as possible. Accommodations usually require a medical diagnosis. Some can be significant yet temporary in nature, such as a concussion, or a sprained wrist that impacts your ability to take notes. Others can last the entire term, such as PTSD or dyslexia. If you think you might have a condition that qualifies, please make an appointment with Kara Fifield as soon as possible. Contact Kara Fifield by email or phone, or 847-735-5167. For more information about services for students with disabilities at Lake Forest College, see the webpage. Students are expected to set up their own testing and notetaker accommodations. Please contact Stephanie Edgar, Coordinator of the Center for Academic Success,, for assistance.

Description of instructional time and expectations:

This course meets 3 times per week for 3.0 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Last modified on October 24, 2022.