How to Make a Mobius Strip

Mobius Strip

Mobius strip made from paper.
Mobius strip made from paper.

What is a Mobius Strip?

A Mobius strip, or Mobius band, is a continuous band with only one surface and only one edge. It was discovered by the 19th century mathematician August Ferdinand Mobius, although the discovery of the Mobius strip was first publicized by Johann Benedict Listing, who discovered the Mobius strip independently of the original discovery.

Is it difficult to visualize how a band can only have one side? Follow the steps below to make your own Mobius strip and experience its properties first-hand.

How to Make a Mobius Strip

To make a Mobius strip, you will need paper and scissors, as well as some glue or tape.

1. Cut a narrow strip of paper, around 5 cm in width and half a meter in length.

2. Stretch the paper out between your two hands. Hold end one steady and turn the other end over 180 degrees, putting a twist in the paper strip.

3. Glue or tape the two ends together.

4. Take a pencil and place the tip in the center of the strip. Trace a line lengthways along the strip. Keep going until you reach your starting point.

The fascinating thing that you will notice is that your pencil line covers both sides of the paper - yet the tip of your pencil never left the paper while you were drawing! This is proof that the Mobius strip has only one side.

As a further experiment, take a pair of scissors and cut along your pencil line. What do you get? If you're tempted to answer "two loops," try this practical exercise for yourself - you might be surprised at the result...

Practical Applications of the Mobius Strip

Mobius strips are used as conveyer belts, connecting wheels in a machine. They last much longer than normal untwisted loops as each side of the material gets the same amount of wear and tear. Recording tape is also sometimes looped into a Mobius strip, which gives twice as much recording time as a single loop.

Mobius strips fascinate topologists - mathematicians who study 3D shapes and spaces. Topology has many applications, and the applications of topology aren't only restricted to math and physics. It can even be applied to the theory of music, in which the Mobius strip plays a surprising role: the topological space representing all two note chords (dyads) has the shape of a Mobius strip. This topological representation of musical chords helps theoretical musicians to better understand the principles of music.

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Comments 2 comments

annart profile image

annart 4 years ago from SW England

I've seen one of these before but this is a fascinating description and explanation. For one who's neither scientific nor mathematical I found it strangely interesting! Well done for that! I feel there is a lot more behind this phenomenon - can we have more about his please?! Voted up and awesome (I don't use that very often as it's more of an American word to me - no offence US!).


krillco profile image

krillco 4 years ago from Hollidaysburg, PA

very cool, very educational

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