# Math 340. Geometry

Fall 2022

• Instructor:         Enrique Treviño

• Lectures:           MWF 9:00 - 9:50 pm in BR 121

• Office Hours:    MWF from 8am to 9am, MF from 10-11am, TR from 8:30 to 9:30am, and by appointment.

• Office:               Brown Hall 123

• Email:

• Phone Ext.:        #6187

Announcements

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.

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

• Learn basic Euclidean geometry.
• Learn to use Cartesian coordinates to prove geometric statements.
• Learn to use vectors to prove geometric statements.
• Learn how to come up with a proof on their own.
• Learn basic projective geometry.
• Get exposed to non-Euclidean geometry.

Textbook

The Four Pillars of Geometry by John Stillwell.

Topics we will cover

• Straightedge and compass constuction.
• Euclidean geometry, in particular the geometry of triangles and circles.
• Analytic geometry (using coordinates).
• Vectors and using linear algebra in geometry.
• Perspective
• Transformations
• Non-Euclidean Geometry
• Projective plane (if time permits)
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%.

Homework

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.
Exams

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
• The first midterm will be given on Friday September 16 and due on September 23. Feedback on September 27. Resubmit by September 30.
• The second midterm will be given on Friday October 28, due on November 4. Feedback on Nov. 8. Resubmit by November 11.
• The final exam will be given on Monday November 28, due on December 5. Feedback on December 6. Turn in the final product by Tuesday December 13 by 11am.

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