Math 340. Geometry

Fall 2016

Instructor: Enrique Treviño
Lectures: MWF 10:00 - 10:50 pm in Young Hall 207
Office Hours: MW between 11 to 12:00 pm, and W from 2:30 to 3:30pm. You can also arrange a meeting by appointment.
Office: Young Hall 105
Email:
Phone Ext.: #6187

Announcements

The videos to watch this week and the questionnaire to answer is below in the Videos and Questionnaire section.

Midterm 1 Solutions. The first three problems are known as "Power of a Point". The fourth problem is a classic equation. The fifth problem is Ptolomy's Theorem and the solution is over 2000 years old. The sixth problem is known as Brahmagupta's Formula. The seventh problem is a classic problem where Ptolomy's theorem needs to be applied. The Bonus problem comes from the 2001 Mexican Mathematical Olympiad. This was one of the four problems I solved (out of 6) to earn a Gold medal at that competition.

Worksheet 1 to work on during the week of September 26 to September 30 in class.
Worksheet 1 Solutions.
The worksheet has a proof of the Euler line. Here is Euler's original paper in Latin and William Dunham's explanation of Euler's proof in English. The pdf with Dunham's summary also contains a very clever short trigonometric proof of Heron's formula. You can compare to the proof in the worksheet (problems 4 through 8) and compare which one is an easier proof.

Midterm due next Friday (September 23) in class.

Homework 3 now online.

The following Scientific American article written by Evelyn Lamb contains the diagram of president Garfield's proof of the Pythagorean theorem (proof 3 in class) and a diagram from an ancient Chinese book (probably from 1 B.C.E) that actually proves the Pythagorean theorem in two ways (proofs 1 and 2 in class).

This New Yorker article written by Steven Strogatz gives a very nice background (and explanation) on Einstein's proof of the Pythagorean theorem (proof 5 in class). 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

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.

Grading

The course grade will be based on:
Homework 48%,
Questionnaire 5%,
Class Participation 8%,
Midterms 24% (12% each),
Final Exam 15%.

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 26. Resubmit by September 30.
The second midterm will be given on Friday October 28, due on November 4. Feedback on Nov. 14. Resubmit by November 18.
The final exam will be given on Monday November 28, due on December 5. Feedback on December 7. Turn in the final product by Monday December 12 by 11am.

Videos and Questionnaire

The week of November 6 to 11, I will be attending the Mexican Mathematical Olympiad. There will be no class sessions. As a substitution, I will assign you to watch several videos related to Geometry. The list will be displayed here later. As part of the week, you will have to answer a questionnaire that will have questions related to the videos you will watch.

Videos to watch:

Elliptic Pool Table. You can also watch the compannion piece A game for the elliptic pool table.
How to trisect an angle in origami. I also recommend seeing the video Euclid's big problem for yet another exposition of straight-edge and compass.
The math and magic of origami.
All triangles are equilateral.
Ditching the fifth axiom.
Math and movies (animation at Pixar).
Playing sports in hyperbolic space.
The three square geometry problem.

The required videos add up to 76 minutes and 45 seconds of screen time. If you watch the two extra recommended videos, it would be a total of 89 minutes and 27 seconds.

Questionnaire.

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. I will also take points off for falling asleep or using a smartphone (or a laptop) in class.

Accommodations Statement

If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit http://www.lakeforest.edu/academics/resources/disability/.

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.

Last modified on November 22, 2016.