## MATH 308, Section 101: Euclidean Geometry

### Announcements

The first three pages of the final exam have been posted, including the fact sheets that will be included in the final.

The solutions to the study questions for the final exam have been posted.

Solutions to Homework #8 have been posted. Also, you may pick up your marked Homework #8 outside my office.

The final exam will be on Thursday, December 16 from 8:30-11:00 AM in the “A” wing of the Buchanan building, BUCH A102. For the exam, all you need to bring is your student ID and something to write with. Remember that there will be no makeup exam.

For the exam, all the paper you need will be provided for you. No notes, books, calculators, or other aids are allowed; please do not bring cell phones, pagers, alarm watches, or anything else that would make noise during the midterm. You may wish to ensure that you are familiar with UBC's Academic Regulations pertaining to misconduct during exams.

• for Friday, September 10: pages ix, xiv, and 1-14
• for Monday, September 13: through page 17
• for Wednesday, September 15: Sections 1.4 and 1.5
• for Friday, September 17: Section 1.6 (recommended: Exercises 1.25, 1.28, 1.30, and 1.31)
• for Monday, September 20: Section 1.7 (recommended: Exercises 1.35, 1.41, and 1.43)
• for Wednesday, September 22: Sections 1.8 and 1.9 (recommended: Exercises 1.50, 1.52, and 1.68)
• for Friday, September 24: Section 1.10 (recommended: Exercises 1.45, 1.53, 1.72, 1.75, and 1.78)
• for Monday, September 27: Section 1.11 (recommended: Exercises 1.67, 1.89, and 1.92)
• for Wednesday, September 29: Sections 1.12 and 1.13
• for Friday, October 1: Section 1.15 (recommended: Exercises 1.121, 1.122, 1.123, and 1.124)
• for Monday, October 4: Section 2.3
• for Friday, October 8: Sections 2.1 and 2.2 (recommended: Exercises 2.6 and 2.7)
• for Wednesday, October 13: Sections 3.1-3.3 (recommended: Exercises 3.1, 3.3, and 3.6)
• for Friday, October 15: Section 3.4 (recommended: Exercises 3.9 and 3.10)
• for Friday, October 22: Section 3.6 (recommended: Exercises 3.32, 3.33, 3.34, 3.35, 3.4, and 3.11)
• for Wednesday, October 27: pages 115-119 (recommended: Exercise 6.1)
• for Friday, October 24: Sections 6.3-6.7, concentrating on the definitions and facts stated
• for Wednesday, November 3: Sections 6.3-6.4 (re-read)
• for Monday, November 8: Sections 7.1-7.2 (recommended: Exercise 6.9)
• for Monday, November 15: Sections 7.3 and 7.6 (recommended: Exercises 7.1, 7.2, 7.35, 7.37)
• for Wednesday, November 17: Section 7.4
• for Friday, November 19: Sections A.1 and 7.5 (recommended: Exercise 7.28)
• for Monday, November 22: Sections 5.1, 5.2, and 5.3 (recommended: Exercises 5.1, 5.2, 5.3)
• for Wednesday, November 24: Sections 5.4 and 5.5 (recommended: Exercises 5.10, 5.14, 5.15)
• for Monday, November 29: Section 7.7 (recommended: Exercise 7.46)
• for Wednesday, December 1: Sections 7.13 and 7.14
• Here is a nice link where you can play with the Platonic solids.

There are some fun and intuition-helping Java applets of the disk-model of the hyperbolic plane on the web. Although you can find many yourself, I liked this one, especially the first two links - "the hyperbolic plane" and "experiments in hyperbolic geometry". Play with them for a bit, and you'll really understand these models of hyperbolic geometry better!

There is a nice annotated version of Euclid's elements online.

Homework Assignments Solutions to Homeworks Miscellaneous Handouts
Homework #1 Solutions #1 Course Outline
Homework #2 Solutions #2 Study Questions for Midterm 1
Homework #3 Solutions #3 Solutions to Study Questions 1
Homework #4 Solutions #4 First pages of Midterm 1
Homework #5 Solutions #5 Solutions to Midterm 1
Homework #6 Solutions #6 First pages of Midterm 2
Homework #7 Solutions #7 Study Questions for Final
Homework #8 Solutions #8 Solutions to Final Study Questions
First three pages of final exam

### Course Information

When: Mondays, Wednesdays, and Fridays, 11:00–11:50 am
Where: MATX 1100 (Mathematics Annex)
Textbook: A. Baragar, A Survey of Classical and Modern Geometries (Prentice Hall)
Prerequisites: A passing mark in one of MATH 221, MATH 223, or MATH 152; and a passing mark in one of MATH 220, MATH 226, or CPSC 121. The second prerequisite is extremely important, and students who have not passed MATH 220, MATH 226, or CPSC 121 will typically be significantly unprepared for this course. Virtually all of your course work will be understanding and writing proofs.

Instructor: Prof. Greg Martin
Office: MATH 212 (Mathematics Building)
Phone number: (604) 822-4371
Office hours: Tuesdays 10:00-11:30 am and Fridays 2:00-2:50 pm

Description: We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, triangle congruences and centers, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry (axioms) and the proofs of these results. Towards the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry, a type of non-Euclidean geometry that can still be visualized.

We will also mention, to some extent, the historical evolution of the subject of geometry, the geometry of polyhedra in Euclidean (three-dimensional) space, and isometries and tilings of the plane (e.g., wallpaper patterns). The material we will be covering is essentially Chapters 0-3 and 5-8 of the textbook, with possibly one or two brief handouts for supplementary material. In summary, the emphasis of the course will be on a rigorous understanding and exposition of the subject, proof-based and abstract (as opposed to computational).

Use of the web: All homework assignments and other course materials will be posted on this course web page. After the first day, no handouts will be distributed in class. You may access the course web page on any public terminal at UBC or via your own internet connection. Accounts for the Mathematics department undergraduate computer lab (located in the MSRC building) will be given to any enrolled student who requests one; please email or visit the instructor to request an account.