Geometry Project - Presenting Mathematics: Extended Topics in Geometry
The goal of this project is to explore some advanced topics in geometry, and to present your topic to the class, including a presentation of mathematics.

Expectations are as follows:
1. You should research a mathematical topic related to geometry (subject to my approval) and learn as much as you can about it. The culmination of your research will be a presentation to your classmates which summarizes what you have learned.

2. The presentation should be approximately 20 minutes. You may use slides if you like, but you can also give a "chalk talk". Pictures, props and handouts are all encouraged (keep your audience engaged!).

3. Your goal in your presentation is to inform your classmates about the topic you researched. This means it needs to be accessible (define anything we haven't talked about in class), but also go into some depth in the topic. In particular, it should include some detailed mathematics (such as a proof of a theorem).

4. To thoroughly research your topic, you should use several sources. Include in your presentation a list of references. A complete project should include at least three sources, which may or may not include our textbook.

5. You should submit a title and abstract (a short paragraph describing what you'll talk about) by Thanksgiving break (by Monday, November 24). These will be posted for the rest of the class prior to the beginning of talks.

Class attendance will be required during presentations. A grade (equivalent to one homework assignment) will be given for participation. You should come prepared to ask your classmates questions!

If you're interested in writing a slide presentation using LaTeX, try this Intro to Beamer. My personal webpage also includes some samples of presentations using beamer.

Presentation Schedule and Abstracts

Monday
11:00-11:12	Audrey Gomez
11:15-11:27	Rachel Ayersman	The Geometry of the Universe: Is the Universe Finite or Infinite
		We will review different possible finite models for our universe. We will discuss how a finite model can be boundless with examples such as the torus model. We will define the term curvature and explain it use in helping astronomers determine the shape of the universe. Finally we will explore a more popular model for the universe: Poincare Dodecahedral model.
11:30-11:45	Jill Isaacson, Rachel Krebsbach, and Olivia Murphy	Introduction to a Sierpinski Fractals
		Sierpinski fractals are iterated function systems, a branch of fractal mathematics, that describe successive containment of geometric shapes. The primary purpose of this investigation is to examine Sierpinski triangles and their mathematical relations. Sierpinski carpets and pentagons will also be touched on.
Wednesday
11:00-11:15	Matt Pancoe and Tyler Reuter	The Curvature of the Hyperbolic Plane
		We will find that in order to represent hyperbolic lengths by Euclidean lengths our model must be isometric, and we will explain what that means. We will explain how hyperbolic planes are repesented, namely, by geodesics. We will explain, through the use of a Hilbert theorem, that it is impossible to embed the entire hyperbolic plane isometrically as a surface in Euclidean three-space, but the contrary is possible. With consideration of a horocyclic sector we will show the previous statement works in both directions. We will talk about Dini's surface.
11:17-11:32	Emily Stephenson and Julia Faherty	Equiangular Dodecagons
		We will be investigating integer equiangular dodecagons, properties of them, and how to compose them using only squares, equilateral triangles and 30 degree rhombuses.
11:35-11:50	DrieAnn Peterson and Liz Burianek	Mobius Strips
		In our presentation, we will be discussing the Mobius Strip. A few areas we will cover will be: where it is created; how to create one; and the restrictions on creating one. We will also have an activity in three-dimensional space, as well as examples we have previously made, to demonstrate the re- strictions. Finally, we will share some real world applications of a Mobius Strip.