Exploring a Mobius Strip

The magic circle, or Mobius strip, named after German mathematician, August Ferdinand Möbius, is a loop with only one surface and one edge. Impossible? Let’s explore this to find out more.

Make a Mobius stripStep 1: Cut a strip of paper. An easy way to do this is to fold an 8 ½” x 11” sheet of paper in half lengthwise. Cut along the fold. Tape the narrow edge of one strip to the narrow edge of the second strip, forming one long paper strip.

Step2: Hold the two ends in your hands, give the strip a half twist and tape together the short ends. Now you have a Mobius strip.

Exploring the stripStep 3: Now take a pen and starting at any point, draw a line along the middle of the strip, continuing all the way until you reach your starting point again. You have drawn a line on both sides of the loop—but without lifting your pen or crossing any edge. The paper has only one side!

3Step 4: Now take a highlighter and color the edge of the strip. Just like you did with the pen, keep coloring the edge without lifting the highlighter. You’ll find both edges are colored. But you didn’t switch edges. How is this possible? Is this really just one continuous edge? What unique features are you discovering about this loop of paper?4Step 5: Now with scissors, cut the Mobius strip along the central line you drew earlier. What do you predict will happen as you complete cutting along the entire length of the center line?

Did the results turn out as you had expected? What had you expected?

What was the actual result? 5Step 6: What other things would you like to try? Cut the loop a different way? How? Fold it? How? Feel free to experiment with this loop in more ways or to create a new one to explore with.

For further exploring:If you are enjoying this exploration and want to check out some on-line demonstrations and discussions of the Mobius strip, here are some options to start with:

http://science.wonderhowto.com/how-to/craft-mobius-strip-out-paper-316736/ Scroll to the middle of the page for this You Tube. It is a video description of the lesson activity in this handout.

http://www.youtube.com/watch?v=9PN4gyxpH2M This You Tube segment has notes about how this concept is used in the real world, not just in math concepts.

http://www.youtube.com/watch?v=0gOorunbCfw This You Tube segment discusses a little more about the concepts that evolved from the Mobius explorations, math, and geometry concepts.

http://www.youtube.com/watch?v=4mdEsouIXGM This You Tube segment is a creative use of a clear mobius strip as a tool for storytelling.

STEM skills in actionAs you created and explored the Mobius strip, think of all the STEM skills you were using: cutting and aligning shapes (geometry), processing instructions, putting materials together (design/engineering), predicting, observing, data collection, analyzing, testing, use of tools (science) and additional on-line research (use of technology and science).

These instructions have been modified from the document: http://www.wikihow.com/Make-a-Mobius-Strip, edited by Lawreadaholic, Teresa, Harri, SilverSparkz, and one other and shared with permission under the Creative Commons License

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HO_C2S_Mobius_r1–May 12, 2015