Final Term Paper Details
There is no final exam in Fall 2021 Mathematics 435:01. In lieu of an exam there will
be a final term paper due on 12/22/21 (by 11:59 PM) which will be submitted via the
Canvas site for the course.
The paper should be about 5-10 pages double-spaced, including a bibliography. This
should be around 2000 words or more. Papers must be submitted by the due date 11:59
12/22/21. The paper will contain your clear discussion of a topic in geometry that you
have researched. You can include sketches that explain the geometry you are writing about
by scanning a drawing that you make.
A list of possible projects is given below. You can also propose your own topic. Email
me with your topic when you have chosen it.
Your paper should be a double-spaced typewritten document, which will be submitted
online in Canvas as a PDF file. Follow accepted form for a term paper, writing in complete
sentences, providing citations to references and a bibliography at the end of the paper.
Due to the pandemic much of the references will be to online sources, so you should
make sure that you cite these in acceptable form.
A large part of your paper might be mathematical in nature. In this case, you will
probably want to include formulas and short derivations/ideas. (Longer proofs do not
belong in a piece of exposition but you may want to cite a resource which contains them.)
The typical way to include formulas in typewritten works is to use a program like LATEX,
but LATEX has a steep learning curve. Handwritten formulas and formulas typeset using
Microsoft Word or similar will also be accepted. (The bulk of the paper should still be
typewritten, however.) The project must consist of your own work. Plagiarism will be
reported to the Office of Student Conduct and could lead to automatic failure of the
course. When in doubt, cite your materials.
The goal of this term paper assignment is to analyze a topic in detail and to provide
an exposition of the topic accessible to others. Some introduction to topics is in our text,
but you will have to use several other sources as well for your paper. You may assume the
theorems and definitions contained in the text or lectures.
Grades for the paper will involve the following criteria:
General standards as a term paper: Is your paper accurately cited, does it match the
formatting guidelines, and is it your own work?
Overall quality of exposition: Has an effort been made to make your paper accessible
to the reader? Does it give enough background and is it edited well?
Overall quality of analysis: A good paper should cover explanations in addition to
facts. Does the paper address the why in addition to the what? Don’t just state
things. Explain why they are true.
Quality of technical writing: Are the mathematical sections in your paper clear,
convincing, and correct? Are sufficient details provided for the reader to appreciate
the mathematics?
SUGGESTED FINAL TERM PAPER TOPICS
You are free to suggest your own topic, or to choose one in the list below or suggested
by it. Send me email when you’ve decided on a paper topic so the topic can be noted and
we can make sure that everyone is not doing the same topic.
Euclidean Geometry topics
1. Napoleon’s Theorem on triangles (the only math theorem attributed to an Emperor!)
2. The Euler line and Pascal’s theorem
3. Monge’s theorem
4. The nine point circle of a triangle – The 3 midpoints of each side of a triangle, the 3
feet of each altitude and the 3 midpoints of the line segment from each vertex of the
triangle to the intersection of the three altitudes all live on a circle
5. Conway’s circle theorem-when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line
segments lie on a circle
6. Morley’s theorem – The three points of intersection of the adjacent trisectors of the
angles of any triangle form an equilateral triangle.
7. Compass vs straightedge – all Euclidean constructions can be done with a compass
alone
8. Polarities of conics
9. Apollonian circles
Non-Euclidean (or hyperbolic) geometry topics
10. Hyperbolic rotations
11. Hyperbolic geometry and the drawings of M.C. Escher (see Stillwell page 195
12. Tessellation of the hyperbolic plane and Euclidean plane
13. Constructions in noneuclidean geometry
Spherical Geometry topics
14. Spherical trigonometry -law of cosines, great circle routes
Projective Geometry topics
15. Perspective and art – where should the viewer stand at the art museum?
16. Application of projective geometry in computer graphics