Fall 2010 Math 471 – Research Project
Guidelines:
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Work in groups of 2 people. (If there are an odd number of people, there can be one
group of 3 people.)
This research project is worth 80 points.
You may choose a topic from the available list, or different topics can be chosen as well. .
I will make sure that we have as many different topics presented as possible - If more
than one group chooses the same topic, then it will be dealt with on a first-come-firstserved basis if necessary. (Most topics are broad enough that we can vary the emphasis of
the project.) There is also a list of a few general links to non-specific topics at the bottom
of the page that may help in deciding a topic or locating internet resources.
There will be a written component which accounts for 60 points. (The rough draft is
worth 20 points, and the final draft is worth 40 points.)
There will be an oral presentation which is worth 20 points.
You must meet the deadlines for each portion to receive maximum credit.
DO NOT PLAGIARIZE. You are probably researching ideas and theorems that have
been known for a long time, so just like in any research paper, you should read a variety
of resources on the topic, decide what you want to focus on, and then convey your
understanding of what you read in your paper in your own words.
Written component
DO NOT PLAGIARIZE. Different projects may require different formats, but here are few
general guidelines that would apply to most projects.
The length of your paper is not pre-set, but generally I would expect 6 -10 pages (more if you
have many pictures).
(I) An introduction - It should contain a general idea of what the topic is about and what the
major focus of the paper is. Anyone in the class who reads it should be able to have a general
understanding. (You can also include some general applications, some history, and other
motivational information.)
(II) The body of the paper - this may be several sections. This should lead the reader to the
major focus of the paper in more detail. You should state and describe necessary notation,
definitions, and theorems and clarify them with illustrations and examples. Lead up to your
major results and then stress their importance with specific applications and interesting
consequences.
(III) Conclusion - a general discussion about what geometry you learned and applied.
(IV) A reference page. There are a few web resource links below that may help get you
started. You must include internet resources on your web page.
Oral Presentation
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All group members must present.
Each group member should have equal time and equal opportunity to present significant
information.
On the day of the presentation, each group will turn in two questions that relate to the
main emphasis of the project and that they would like everyone in the class to understand
when they are done presenting.
The amount of time available to present will depend on the class size, but generally it will
be between 10 and 20 minutes.
Grading
There are three different components to the overall grade.
1) Rough draft - 20 points. Should include parts (I) and (IV) under the written
component of the guidelines and some work in (II). In other words, it should be clear that you
have found valid references, that you have decided on the major focus of your paper, and that
you have at least a well thought out outline of the body of your paper.
2) Final Paper - 40 points. There are many factors that affect this grade, but the main
one is that I can tell in reading your paper that you learned some mathematics outside the
classroom and you used your own words in explaining your understanding of the topic. Be sure
you have referred to the written component guidelines.
DO NOT PLAGIARIZE. If you include someone else's work, then make sure that you give
them the credit. You are probably researching ideas and theorems that have been known for a
long time, so just like in any research paper, you should read a variety of resources on the topic,
decide what you want to focus on, then convey your understanding of what you read in your
paper in your own words.
Example: If you have an important theorem you want to prove or are explaining something with
detailed mathematical language; it is not expected that you come up with an original proof of a
theorem, but it is expected that you use your own words in explaining the proof and that you
show understanding by filling in details and/or including your own pictures and/or including
your own examples.
Other factors include organization, clarity, reference choices.
3) Oral Presentation - 20 points.
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Your group should take 10 – 12 minutes to present the major focus of your paper and
demonstrate your understanding of the topic.
On the day of the presentation, each group will turn in two questions that relate to the
main emphasis of the project and that they would like everyone in the class to
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understand when they are done presenting. Please bring enough copies for everyone.
These questions will help me see if you have focused on the main content of your paper.
The class and I will ask questions of each member of the group. This is where I will
determine your understanding of the topic. I am allowed to ask questions from the paper
that you may not talk about in your oral presentation.
Deadlines
Tuesday, September 14: Have group members determined
Tuesday, September 14: Have topic selected
Tuesday, October 19: Rough Draft Due
Tuesday, November 16: Final Papers due
December 7 and December 9: Presentations. Turn in two questions.
Possible Topics
These are just a few possible topics.
1) Fractals - self-similarity
2) Three-dimensional Transformations
3) More Non-Euclidean Geometry - wide open but could include things like
tessellations on the sphere and/or hyperbolic plane
transformations on the sphere and/or hyperbolic plane
Three-dimensional Non-Euclidean geometry
Applications of Non-Euclidean Geometry
Investigate other geometries that were not discussed in class
4) Polyhedrons - classification, symmetry, Schlegel diagrams
5) Algebraic curves - equations and curves, singular points, blow-ups
6) Geometry with Complex Numbers - relate the use of complex numbers to triangles,
quadrilaterals, and any of the many theorems we talk about in class.
7) Projective Geometry and how it's related to Euclidean Geometry- wide open, but could
include popular theorems like
a. Pascal’s Theorem and Brianchon’s theorem (For a circle)
b. Pappus’ Theorem
8) More Euclidean Geometry - wide open, but here are a few "name" theorems and other
ideas (There are many other "name" theorems as well)
a. Pascal’s Theorem and Brianchon’s theorem (For a circle)
b. Stewart’s Theorem
c. Morley’s Theorem
d. Pappus’ Theorem
e. Desargues’ Theorem
f. Ptolemy’s Theorem
g. More triangle centers
h. More collinear points related to a triangle
9) Strip patterns, Friese patterns and their groups
10) Tilings (tessellations) of the plane and space - regular and semi-regular, symmetry
groups
11) Your own investigations of a problem that interests you.
12) Others
A few general links
http://mathforum.org/ - will link to many educational sites and other resources.
http://www.geom.umn.edu - University of Minnesota Geometry Center - A research and
education center.
http://archives.math.utk.edu/topics/ - Archives to many sites organized by topic.
http://www.math.msu.edu/~winter/ - Someone at Michigan State who keeps a nice list of
Mathematics and Geometry links