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How to Make a Mobius Strip
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.
Interesting Math Topics
- Noether's Theorem
Noether's Theorem says that for every continuous symmetry, there is a conservation law. But what is symmetry? And how does this law predict the physical laws of energy conservation and momentum conservation?
- Proof that Root Two is Irrational
Proving that the square root of two is irrational is an example of a proof by contradiction. The basic method is to suppose that square root two is rational and then show that this leads to a contradiction (an equation that is obviously not true).