Math 621: Elementary Geometry


Presentations


On this page you will find information about the final presentations. This will include possible topics and resources.


Presentations will be given during the last 2 weeks of class: 26 Nov, 28 Nov, and 3 Dec. All students are required to attend all presentations. Attendance and participation during your peers' presentations will factor into your grades. The final exam may contain questions from some of the presentations.



Presentations may be done individually, or in groups of 2 or 3 students. There should be a maximum of 9 "groups." (There are 15 students in the class.) Presentations should last about 20-25 minutes per group, give or take a few minutes.

Below you will find a list of possible presentation topics, and the presentation schedule. Both the topics and times are "first come, first served." Email me or message me in Slack to make your reservations!

Presentation Topics

1. (S. Brennan, E. McGettrick) Exercise 1.4.9.

2. Exercises 1.4.10 and 1.4.11.

3. (Y. Wang) Explain in detail the construction of Example 1.5.1. In particular, explain why angle \(A\) has the correct measure.

4. (J. Minnick) Present the details of Euclid's proof of the Pythagorean Theorem (section 1.7, proof 2).

5. (E. Page, L. Peterson) Exercise 2.3.15.

6. (L. Chau, J. Smith-Bell, M. Rangel) Exercise 2.5.7.

7. (D. Ludlow) Exercise 3.2.4.

8. Let \(C(\rho)\) be a cicle centered at \(C\) with radius \(\rho\) in the complex plane \(\mathbb{C}\). Derive a formula for the inversion \(I_{C(\rho)}\) in complex coordinates.

9. (A. Craig, A. Hamner, A. Yoder) Present and prove Pappus's Theorem (Theorem 3.5.2).

10. Present and prove Theorem 3.5.3.

11. Present the Klein Disk and Poincare Ball models of hyperbolic geometry, and describe their relationship to one another.

Presentation Schedule

Wednesday, 28 Nov #1: L. Chau, J. Smith-Bell, M. Rangel, #6
Wednesday, 28 Nov #2: D. Ludlow, #7
Wednesday, 28 Nov #3: A. Craig, A. Hamner, A. Yoder, #9

Monday, 03 Dec #1: S. Brennan, E. McGettrick, #1
Monday, 03 Dec #2: E. Page, L. Peterson, #5
Monday, 03 Dec #3: Y. Wang, #3
Monday, 03 Dec #4: J. Minnick, #4

Assessment

After you have completed your presentation, please complete this assessment survey.




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