Honors Interdisciplinary Seminar
(175)
Fermat's Last Theorem
Assignment
following Week #8 (Due 11/9 in class)
(Section 004 - Due 9/28 in class)
-
Spend at least 30 minutes on the "Constructions" worksheet from class.
Review the constructions we did, and try to finish those that we did not get
to.
- Read
the excerpt from Maor on the Pythagorean Theorem (See "Pythagorean theorem,
p. 1-31" on
ereserve). As you read,
think about the issue of truth. Do the Pythagoreans remind you of
Flatland at all?
- Carefully
read the background material on Fermat’s Last Theorem.
You can find most of the material on
ereserve in the subfolder entitled "Fermat readings."
The packet of material contains four articles from the New
York Times. There is a separate article from the MAA Focus,
a mathematician’s newsletter that you can get here
or from D2L. Pay
very close attention to the dates on the articles, but don't worry about the
section entitled "The Technical Details." I recommend
printing the articles for easier reading and note taking.
- Complete
the Study Questions below.
- With
your group, prepare your proof of the Pythagorean Theorem that you will
present at our next class meeting. You
can find a copy of all the proofs of the Pythagorean Theorem
here or on D2L.
- Read
any emails I send you, and respond if requested.
- There
may be a brief quiz at the start of our next class meeting.
Study
Questions
Please carefully write out your answers to these
questions. Make a copy of your answers and be prepared to hand that copy in at
the start of class. Look at the Study Questions
Main Page for general guidelines on study questions in Steve's section.
Follow-up on
Euclidean Constructions:
- Given
the following triangle:
Construct a copy of this triangle
(with a straightedge and compass) onto your homework sheet.
Carefully list your steps (leave your construction marks), and argue that
your construction is correct.
From the Fermat
readings:
- Write
definitions for each of the following terms: conjecture, theorem,
proof, corollary, and counterexample.
- Carefully
state Fermat’s Last Theorem.
- To
what “familiar” Theorem is it related and how?
Name and state this Theorem.
- Who
was Fermat and what prompted his conjecture?
Why is it really his conjecture
and not his theorem?
- Make
a brief timeline of the story of Fermat’s Last Theorem.
Include both Fermat and Wiles, and for Wiles, include the relevant
aspects of his journey. (Your
timeline doesn’t have to be to scale!)
- Does
the story of Fermat’s Last Theorem change or confirm your view of
mathematics and mathematicians? Why
or why not?
- What
does the story of Fermat’s Last Theorem have to do with truth?
Thinking ahead:
- Come up with one potential topic for your Final Project debate
(see the
Final Project Page for details). Your topic should be an issue related to
our class discussion that can reasonably be debated. Give a brief (just a few
sentences) description your potential topic, including a description of both
sides of the issue. You are not committed to this topic.