Homework

From class on Wednesday, November 29, read section 7.7.

Problem 12 is really just a warmup for problem 13, which is the main focus of this assignment. Try these problems first by yourself, gathering enough data to make a hypothesis about what happens in each case. Then check with one or two other students to see how your hypotheses compare, and try to combine them. Then test your hypothesis on several more examples.

Turn in enough examples to convince a skeptic that your hypothesis is correct. Write about the process by which you arrived at, and then tested, your hypothesis. This written description of your process should be detailed enough for someone else to recreate your thinking.

- See the play "Proof", at the Wise Family Theater,
Thu.-Sun. Oct. 26-29 (for more information, call 747-5118 or
544-8444);
**OR**rent the 2005 movie of the same name, starring Gwyneth Paltrow and Anthony Hopkins. - Write an essay concerning "What is proof?". What does this mean in math class, and in "real life"? What does the play/movie have to say about this? What does it mean to prove something?

The description of how to build

Your assignment is to take as many of the ideas we used for
visualizing cubes in different dimensions (including 4 dimensions) and
apply them to triangles in different dimensions. At a
**minimum**, fill in as much of the table in problem 16
as you can (the last row, for arbitrary *n* is quite tricky;
don't worry if you don't get it, but *do* look for patterns in
the table), and discuss the slices of triangles of various dimensions.
But also look at all the other ideas we used on cubes, and see how
they work for triangles.

- Find a friend or relative to help you with this. You can do this several times, with several differnt people, but you don't have to. (For simplicity's sake, I will refer to this person as "your friend", even though it may instead be a relative.)
- Explain the "Let's Make a Deal" game to your friend.
- Ask them whether they think one should stick or switch, and why. Get them to explain their reasoning.
- Conduct the experiment, with at least 25 trials of sticking, and at least 25 trials of switching. You should serve as the "host", and your friend as the "contestant". Make sure you are not giving away, consciously or unconsciously, which door has the prize.
- Explain to your friend the theory of why one should switch. Is your friend convinced?
- Interview your friend to find out what she or he was thinking and feeling at each stage of the experiment. Was she or he ever confused? angry? happy? interested? bored? Etc.