Geometry Project - Writing Mathematics: Neutral Geometry
The goal of this project is to explore some problems in neutral geometry that are a little more challenging, and to practice writing and communicating mathematics.

Topic
You may choose any of the "Major exercises" from Chapters 2, 3, or 4 of our textbook.

Work
To begin your project, work through the mathematics of the problem you chose. You may work with a partner on this stage of the project (but the write-up will be your own).

Write-up
You should write as complete as a solution as possible to the problem you chose. Your write-up should be in the style of a math paper that might be published in a journal. That is, it should begin with an introduction to the topic, including relevant context of the problem. It should describe any necessary background for your proof, with references. It should include a complete and clearly written solution to your problem, as well as proofs of any lemmas necessary to support your work. It should conclude with some exposition about the value of the discoveries you made. In particular, you might pose some further questions about your topic that you think would be interesting to explore. Be sure to include a complete bibliography.

LaTeX
When writing mathematics, we often need to use mathematical symbols in our exposition. For this reason, most mathematicians prefer to use LaTeX to write their math. For this project you must write your paper in LaTeX. If you have not used LaTeX before, a great resource for learning the basics is this wikibook. There are lots of other great resources available online, so if you don't like this one, you can google and find a wide variety.

Logistics
Your project is due Nov 3, by class time. You can work with a partner on the mathematics portion, but you should each write up separate papers. Your grade will be determined based on quality of mathematics, quality of exposition, and quality of presentation (effective use of LaTeX).

Other resources
Here are some other resources about working with LaTeX:
• Cloud-based LaTeX computing is available at www.writelatex.com and www.sharelatex.com.
• DeTeXify can help you find a symbol you need to use.
• TeX Stack Exchange is a Q&A site with descriptions of some of the more complicated TeXing techniques.
• The Comprehensive LaTeX symbols list.
• Symbol Search
• A general introduction
• Another brief introduction