The Curious Loop

The magician tries to fit a loop of paper around his wrist but it won’t fit.  The magician says, “Hmmm, I’ll have to cut this loop bigger”.  The magician takes a pair of scissors and cuts the loop in half up the middle.

Normally, you would expect a loop cut in half up the middle to turn into two loops, instead of two loops, the magician ends up with one larger loop that now fits around his wrist!

 

BEFORE YOU DO IT…

You’ll need some paper, sticky tape and scissors

Take a long, fairly wide strip of paper.  Twist the paper once and tape it into a loop.

This type of loop is called a “Mobius Strip”.

mobius

 

TO PERFORM…

Snip the loop up the center.

Don’t go too fast and keep as close to the exact center as you can.

You can utter some mysterious magic words as you go – or maybe tell them how The Mad Hatter himself taught you this amazing mystery!

When you’re done cutting, you’ll end up with one big loop with a couple of twists in it — the natural assumption is that you’d end up with two loops.

mobius1

 

 

HOW IT WORKS

A loop with a single twist in it is called a mobius strip.  The “Mobius Strip” is an actual mathematical puzzle.  I tricked you into doing math! But it looks like real magic!

The Mobius Strip has several very curious properties.  A line drawn starting from the seam down the middle will meet back at the seam but at the “other side”.  If continued the line will meet the starting point and will be double the length of the original strip.

mobius2

If an ant walks along the edge of the strip, he’ll travel twice as long as the loop before he gets back to his starting point.

Cutting a Mobius strip along the center line yields one long strip with two full twists in it, rather than two separate strips.  This happens because the original strip only has one edge which is twice as long as the original strip.

When you do the trick, you have to be careful to cut as close to the center as you can, because there’s a second magical mathematical ability the Mobius Strip has.  If the strip is cut about a third of the way in from the edge, it creates two strips: One is a thinner Mobius strip, the other is a longer but thin strip with two full twists in it.   So keep your cut close to the center so you don’t accidentally end up with this.

mobius3

As with all tricks, it’s best if you practice this a few times before you do it for an audience!

 

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