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
Phone Ext.: #6187
Midterm 2 Solutions.
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:
The Four Pillars of Geometry by John Stillwell.
Topics we will cover
The course grade will be based on:
Class Participation 8%,
Midterms 24% (12% each),
Final Exam 15%.
Videos and QuestionnaireThe 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.
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.
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.