4.2. April 18, 2002: Magic Cylinder

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

Caveat Lector: This is a web-friendly version of the activity sheet MAGIC CYLINDER. You can also download the file (RTF) for your own use. (RTF is Rich Text Format, which can be opened in Microsoft Word, AppleWorks, ClarisWorks, Okito Composer, TextEdit, Mariner Write, and likely other word processors of varying vintages on varying platforms.)

COORDINATE SYSTEMS: MAGIC CYLINDER

Here are the group roles. We will use the die that Ms. Lee has handed out to our group to decide who gets which role.

Remember, no islands!

highest number
question person/reporter
authorized to ask Ms. Lee or Mrs. Sooy the group's questions

next highest
reader
reads directions and makes sure everyone understands them

3rd highest
materials person
organizes necessary materials and makes sure everyone has something to work on

lowest number
scribe (monitor)
writes notes (keeps everyone on-task)

Today, we will learn about a coordinate system that shows up outside math classrooms: chess.

NOTE: If someone doesn't know how to play chess, don't worry. Everything the group needs to know is in the Chess Box. (It won't make everyone a chess grandmaster--the rules can get complicated--but we're doing math, not tournament chess.) If someone in the group knows how the pieces move, even better.

If anyone does want to play some chess, stay in at lunch and ask to borrow the Chess Box. That's what it's for.

MATERIALS: Before we start, we'll need the Magic Cylinder Book, patty paper, regular paper, and pens or pencils.

Take a few moments to look through the book. Don't write on it and don't lose anything. It's not fair to the people who'll use the book afterward.

1. Read the inside cover as a group before reading the SITUATION and SOLUTION below. Each person should get a chance to see how the magic cylinder works using the designs in the book.

THE SITUATION

You are designing a flag for this class, but you want to make a design that no one can "read" without using a magic cylinder. (Why? You tell me.) This kind of "distorted" picture is called an anamorphism.

HINT: It looks like another strange math word, but what does "morph" mean?

A SOLUTION

Graphics designers sometimes use computer programs to create magic cylinder effects. Unfortunately, you don't have any of those programs (and they take some practice to use). Fortunately, there is a way to do this using coordinate grids.

2. Read pp. 24-26 to find out how the magic cylinder works. Each person should be able to summarize what happens.

3. Using some patty paper (instead of drawing on the book), we will design our flag on the square coordinate system, then transfer the design to the polar coordinate system on a separate piece of paper. Check that the design works by using the magic cylinder.

4. On p.31 there are some more magic cylinder designs. Notice how they're made of straight lines. Discuss ways to make curved lines work for the magic cylinder. Take notes on the discussion and draw an example.

5. If we had a cylinder with a design already on it, how could we draw the "distorted" version on a piece of paper? Discuss ways to do this and draw and example.

6. We will turn in:

• group discussion notes
  
• flag design (before and after)
  
• individual reports
  

Each individual report should say:

• how I contributed to the group, with 2 specific examples, such as "I figured out what happens to straight lines in the magic cylinder" or "I helped design the flag."
  
• a scenario where I might use a coordinate system to describe a game or design, which can't be the same as the SITUATION in this handout
  
• comments from two group members on your contributions
  

Remember:

• 1. Be polite.
  
• 2. Be constructive.
  

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 18 May 2002