# An Endless Story

##### by Natural Math

Do stories repeat?  They most certainly do on a Möbius strip!

The Möbius strip, or Möbius band, is named after August Ferdinand Möbius, a 19th century German mathematician and astronomer who was a pioneer in the field of topology. (The strip was also discovered independently at around the same time by Johann B. Listing.) The unique property of the strip is that it has only one side and only one edge — which also has practical applications in industry where large Möbius strips have been used as conveyor belts (making them last longer as each “side” wears the same), and as continuous loop recording tapes (which double the playing time).

Make your own Möbius strip and use it to create an endless story with this fun activity that connects math with creative writing.

Materials:

• A strip of paper, 1 foot long by 3 inches wide.
• Tape
• A colored marker or pen/pencil
• Scissors
• Optional: stickers for decorating

Activity:

Step 1: Notice the two short ends of your paper strip.  Hold the strip flat. Take one of the short ends, give that end a half twist, and then tape both short ends of the strip together.

Ta-Dah! You have created a Möbius strip!  It has only one side and only one edge!  Remarkable, you say?  Now let’s prove it!

Step 2: Take a colored marker (or pen/pencil). Place the point of the marker midway between the long “edges” of the Möbius strip.  Now draw a line starting from that point all along the center, continuing along the strip until you return to the starting point.

Examine the strip —what do you notice?  Is there any place where the line doesn’t appear down the center?

Step 3: Next, hold one long edge of the Möbius strip against the tip of the marker.  Color the edge of the strip by holding the marker still and just rotating the Möbius strip around.  Does the line ever cross an edge?

Step 4: Now, think of a simple story that repeats (e.g., “I have a seed. I plant the seed in the ground. I water it. It grows into a plant. The plant drops new seeds on the ground. I have a seed. I plant the seed in the ground,” etc.). Write words, draw,  or use stickers to illustrate your own endless story along the center length of your Mobius strip, continuing the story until it returns to its original beginning.  You now have an endless story!

Time for a challenge:

Create another Möbius strip without anything drawn or written on it. Repeat Step 2 above by drawing a line down the center of your strip. Next, use scissors to cut the Möbius strip along the center line. Can you predict what will happen?  Can you create another endless story along this new version?

More Mobius challenges abound:

Start with a new strip of paper.  Try twisting the strip 2, 3, and more times before taping the two short edges together.  Then cut along the center length. What’s  happening?  Can you make more endless stories with these versions?