# Twisted Math

December 10, 2014

We often think of math as something we do, and art as something we create. Imagine how the mind expands when we can physically create math right before our eyes, and then explore the math with our own two hands! Today you can do just that, and all you need is paper, scissors and tape.

What is this magical, simple mathematical creation you can make in minutes? It’s a Möbius strip. Discovered in 1858 by August Ferdinand Möbius and Johann Listing, a Möbius strip is a nonorientable surface, meaning it is three-dimensional but only has one side.

My kids love riddles and challenges, so I started this activity by asking them if they thought they could make a piece of paper with only one side and one edge. The consensus was, “No way!” Despite their disbelief, they were eager to be proven wrong.

To make a Möbius strip, take a strip of paper and give the paper a half twist before joining the edges together with tape.

Once you’ve made your strip, try drawing a line along the strip without stopping. Your line will cover the whole strip without ever having to lift your pencil or turn the strip over! Make another strip without twisting the ends before joining them together and compare what happens when you draw a line on it or trace it with your finger.

Now take a marker and draw along one edge. Are all the edges of the strip colored? Did you ever have to lift your maker? Try it with the untwisted strip and see if you can do it without lifting the marker.

Take your scissors and cut lengthwise through the center of the strip. Instead of getting two separate strips, you get one big loop with two twists!

What I love about making Möbius strips is how the activity can be expanded and adjusted to all different ages, from wee ones up to adults. Even the littlest of hands can twist the paper and trace the path with their fingers. Taping and cutting the paper is a wonderful exercise in fine motor skills. Older kids can decorate their strips with intricate designs, as well as see just how many times they can cut the strips in half.

Can you think of any real life examples where a continuous plane such as the Möbius strip is used? Some conveyor belts take advantage of the one-sided nature of the strips. If you want to go really old school, consider their use in a looping cassette tape (bonus: you can also explain the wondrous concept of the “mix tape” to the kids). By using this math concept in a real life application, manufacturers are able to use the entire surface of a material instead of just one side.

You can also see examples of the Möbius strip in art, such as in the work of M.C. Escher, or in architecture, in the design of the National Library of Kazakhstan. Of course by now, you’ve probably worked up an appetite. How about a snack* of a Möbius strip bagel or Möbius Fruit by the Foot ?

No matter how you twist it, exploring the Möbius strip together is pure math fun!

*Have you seen our latest Food Fun printable? It features fabulous math snacktvities!