Rainy Day Activities are back! This month, we explore the mathematical mystery of the Möbius Strip, which is which is a surface with only one side and only one boundary. By twisting a strip of paper 180 degrees, a circle with an interior and exterior becomes a continuous loop. Click here for a post from last fall showing how Project EXCITE students used Möbius strips to explore the relationship between art and science.
by Loretta Rice
This activity starts small, but can lead to a colorful pile of fun!
The exploration of the Mobius Strip often comes up after discussing topology in math class.
Noun: The study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
The investigation into the Möbius Strip will lead into a lot of questions that need to be answered. “What is going on here?” “How do these connect?” “What will happen if I change this?”
Understanding the relationship between objects and the way the objects are made is what the Möbius Strip is all about.
- plain paper strips
- magic marker
- flat surface to work on
1. Start with a long rectangle. The exact width and length is not that important.
2. Mark each corner in order. (ABCD)
3. Give the rectangle a half twist.
4. Using a piece of tape, join the ends so that A is matched with D and B is matched with C.
: Why does the Möbius Strip have only one side and one edge?
1. Start midway between the edges of a Möbius Strip and draw a line down its center. Continue the line until you return to your starting point. Did you ever cross an edge?
2. Next, hold the edge of a Mobius Strip against the tip of a felt-tipped highlighter pen. Color the edge of the Möbius Strip by holding the highlighter still and just rotating the Möbius Strip around. Were you able to color the entire edge?
3. Now, with scissors cut the Mobius Strip along the center line that you drew. Then draw a center line around the resulting band, and cut along it. Did you predict what would happen?
Now, think about what would happen if you cut down the center of your Möbius strip. An ordinary paper ring cut in half would give you two separate rings, right?
If you cut down the center of a Möbius strip, what happens?
For yet another awesome result, try cutting the strip one-third of the distance from the edge. Have your camera ready to document this surprise!
Modifications for Younger or Older Students:
After some practice you can experiment with different flexible materials to create Möbius jewelry or art work for hanging or framing.
Additional Resources and Links:
Math is good for you
!: The history and theory behind the Möbius strip.
Videos showing the different experiments that can be done with the Möbius strip:
Have you ever made a Möbius strip before?
Since Fall 2007, Loretta Rice has taught math and science courses for Project EXCITE and Gifted LearningLinks. Some of her past courses include: “It’s a Puzzlement,” “Brain Teasers," and the upcoming “The Geometry of Architecture” in Summer 2012. Register here!