Text Transcript of the 15 minute August 2, 2001 Talk

Mathematical Association of America MathFest 2001 in Madison WI

Appalachian State University

Andrew Nestler

Santa Monica College

Thank you for coming. At the end of our talk, we will distribute a comprehensive handout containing various related web page addresses.

Many fans and critics consider *The Simpsons* to be one of the smartest
and most literate shows on the air, with many references to scholars and
academic subjects, including mathematics and its own mathematician,
Professor Frink. One reason for this
is that many of the show's writers are Harvard graduates.
In addition, some of the writers have significant
mathematical backgrounds.

Sarah and I will talk about how we have used *The Simpsons*
to introduce and illustrate substantial mathematics
in college classes. In addition, we have documented all of the one
hundred or so instances of mathematics on *The Simpsons*,
from arithmetic to calculus to Riemannian geometry.
This
catalog is posted on my webpage. The address is on the handout
we'll provide at the end.

First, here is a scene from the 1939 film "The Wizard of
Oz". The Scarecrow has been looking for a brain, and the Wizard is
about to help him out.
**Scarecrow receiving his brain and reciting
the Pythagorean Theorem incorrectly**

Now, here is a scene from *The Simpsons*
**Similar scene from The Simpsons**

$pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling) 1F08 12/16/93:

Clearly the Scarecrow and Homer are attempting to state the Pythagorean Theorem, although they have made 3 errors: they say "square root" instead of "square," "isosceles triangle" instead of "right triangle," and they say that you can start with any two sides of such a triangle. The man in the stall gives a version that is closer to the correct one.

I played this scene on the first day of a pre-calculus class. I wrote Homer's statement on the board and had my students identify and correct the 3 errors. This was a fun, non-stressful and productive way to break the ice and review some prerequisite geometry, and there were other benefits as well. It required students to translate into written English an important result often memorized as simply a^2 +b^2=c^2, which they now see is clearly insufficient. They also see an example of how a mathematical statement can appear or sound true, or authoritative, without being valid, and so they must learn to check their claims very carefully.

Sarah will describe the next activity.
**Sarah**

People ask us how we began using *The Simpsons* in class.
As graduate students at the University of Pennsylvania, we were huge
fans of the show. As we were watching, we noticed
the math references. At the same time, as a TA, I began to think about
how I could motivate and engage my students, especially those who were
math phobic. After I obtained my PhD from Penn,
I began teaching at Appalachian State University and was given
a liberal arts math course to teach. Since I am a Riemannian geometer,
I created a segment on the geometry of the earth and universe.

In a special Halloween episode, there is an entire
segment in which Homer Simpson
enters the third dimension. Without even
being prompted, students
immediately question whether *The Simpsons* live in two
or three dimensions. Hence
this is a great way to begin a discussion of what dimension means
and lead up to the shape of space.

I'll talk about how
I've used it in the classroom setting.
**Part of Homer ^{3}**
segment in Treehouse of Horror VI

There are
equations flying around in the new dimension and Bart
trying to save his father by using an x, y, z axis lamppost sign.

To begin with, the students must pretend that the
Simpsons really were 2D and that
Homer did transform into 3D.
They explore what it is like to be a 2D creature
with help from Davide Cervone's
movies of a cube passing through Flatland.
For example, they are asked what
a 2D Marge would see when a cube passes through her plane of existence at
various angles, how a 2D Marge could pass a 2D Lisa, and what a
2D Marge would have to look like in order to eat or see.
After answering these questions, students are asked to
write a letter from 3D
Homer to 2D Marge explaining what happened to him, including
changes in appearance and mathematical explanations
in their own words, such as Prof Frinks explanation
of the 3rd dimension.
I direct them to
websites containing a
text transcript
of the complete Homer^{3} segment
and a
description of the animation techniques used for Homer^{3}.

The students find this challenging but fun, and come up with creative explanations and great ideas. But, one of the dangers of this assignment is that there are some students who don't take it seriously and come up with explanations that are nonsensical and have no mathematical or logical basis. Since this writing assignment is part of satisfying a writing designator on the course, I ask the students to revise their work, which takes care of the problem. For example, one student had 3D Homer explaining to 2D Marge that he was flying. For revisions, I told the student that I didn't understand what he meant and asked him to explain.

For the next lab, usually 1-2 weeks later, I give the students directions to pretend that the Simpsons had been 3D all along and that Homer had transformed to become a 4th spatial dimensional creature. They answer questions about the 4th physical dimension and then write a letter from 4D Homer to 3D Marge. This motivates a discussion on how we can understand the fourth physical dimension and we examine the shape of space with help from Jeff Week's research and activities.

Even the small details of Homer's
new dimension are mathematically interesting. For example, since the
equation 1782^{12} +1841^{12}=1922^{12}
flies by Homer,
students are led through reasons why it is incorrect.
Notice that the left hand side of this equation is odd
since it is a sum of an even number and an odd number, while the right hand
side is even. Also, it is an apparent counterexample to
Fermat's Last Theorem, which we had discussed earlier in the semester.
On the final exam, I ask students to calculate the left hand side
and the right hand side of the equation on their calculator.
Most brands of calculators will show that the sides are equal.
Students are then asked to resolve the apparent contradiction.

Now back to Andrew...
**Andrew**

The title of our talk comes from
a 1st season episode in which 4th grader Bart Simpson cheats
on a math test and consequently is enrolled in a school for
gifted children.

** r dr r joke ** from Bart the Genius

Now, back to Sarah!
**Sarah**

Imagine two girls at a gifted school playing patty-cake while
chanting digits of Pi:

**Digits of Pi** Lisa's Sax (3G02, 10/19/97)

We have mentioned only a few of the many examples of mathematics
on the Simpsons. The diversity and depth of the mathematics are quite
remarkable, in particular for an animated show.
Because the students laugh,
but then start to ask questions and engage the mathematics on their own,
we can help them
to enjoy learning significant mathematics
with creative classroom activities related to the *The Simpsons*.

While the video format is the most effective and fun for the students in conveying all the information, sometimes audio and/or text combined with some still pictures, or just a verbal description of the relevant portion will do just as nicely and is less distracting.

The is also a
website which has text transcripts of many episodes,
including the Homer^{3} episode. This has been quite
useful to me - that is how I found out about the would-be counterexample
to Fermat's Last Theorem. A Simpsons fan had stopped the video to write
down all the equations flying around. I find the transcripts
quite helpful in order to reinforce learning even when I play
video or audio.

I wanted to mention the
Cyberworld IMAX movie. The movie is
still ^{6}
in IMAX theatres and is actually
a 3D movie.
A
dvd of season 1 of *The Simpsons* is due out in September
^{7}.
with other season releases to follow. Andrew has
compiled a guide of mathematical segments of *The Simpsons* -
it is on the web and the address is on the handout.

To conclude, because it contains so many instances of mathematics,
*The Simpsons* is an ideal source of fun ways to introduce
important concepts to students, to motivate them and to encourage deep
understanding.
Over a period of years, only one of my hundreds of students
commented on an evaluation that using cartoons was "stupid."
Most students find it interesting, entertaining and creative.
Recently a student in evaluations said that "the cartoons
were great and fun ways to get them excited about the mathematics".
And of course that is the whole point of using them!
Thank you.

Handout

2. The show is now the longest running sitcom of all time.

3. The show has won 21 Emmys.

4. Homer

5. The

6. While the movie is no longer in US theatres, it is still playing overseas.

7. DVDs have been released. See thesimpsonsdvd.com

Legal Notice:

This web site is for educational use only. To view this web site, you must agree to these terms. We do not benefit financially in any way from this web site. The images on these pages were taken from episodes of

Disclaimer: This web site, its operators, and any content contained on this site relating to "The Simpsons" are not specifically authorized by Fox.

unique hits since March 21, 2002 at 3:45pm Eastern