Wild About Math!Making Math fun and accessible

27Nov/078

Amazing Math trick with paper, scissors, and tape

Here's something fun, not too heavy on the Math unless you want it to be, and quite remarkable to those who haven't seen this before. You're going to create a Moebius strip, and variations on it, and surprise yourself and others when you see what you get when you cut the Moebius strip in various ways. A Moebius strip is a strip of paper that you tape together at both ends, but before you do, you make a half twist in the strip. Your Moebius strip should look like the one in the picture from Wikipedia.

Here's the first thing you can do that'll be interesting. Take a pen and draw a line along the strip lengthwise, starting anywhere you want to start on the strip. What happens? You end up back where you started, right? That's the first interesting discovery - the Moebius strip has only one side.

Now, here's a trick that'll impress you and your friends. This will work better if you make a fairly long Moebius strip, two or three feet long, so that it's not so obvious that there's a half twist in it. Have your friend watch as you cut along the strip lengthwise, halfway between the two edges. Your friend will expect there to be two strips when you're done. But, guess what? Well, I won't tell you. Try this yourself and see.

Try these other things for more amazing discoveries, and try to guess what will happen before you do the experiment:

1. Take your Moebius strip. Cut the strip lengthwise down the middle as discussed above then, with what you get, cut lengthwise down the middle again. What do you get this time?
2. Keep going with the cutting. Sometimes you'll get one ring, sometimes more than one and, when you get more than one, notice how the multiple rings are connected and pick one to cut lengthwise.
3. Starting with the Moebius strip again, cut lengthwise, but instead of cutting halfway between the edges, cut about a third of the way from one edge to the other. What happens this time?
4. Make a variation on the Moebius strip where you make two half twists instead of one before taping the ends together. Experiment with what you get when you cut that strip down the middle and when you cut it a third of the way from one edge to another.

You can have a tremendous amount of fun with the Moebius strip and its variations. You can create all sorts of experiments just by varying how many half twists you make in the strip, how many times you cut it, and how far between the two edges you cut. If you're going to make lots of twists or lots of cuts I recommend that you make your strip several feet long to start (tape together several strips to get a long one) and several inches wide to make it easier to cut.

Enjoy!

1. There is also a sci-fi mystery novel about the Moebius strip which I wrote this year (2007)and which is the first sci-fi novel using a Moebius strip and a vehicle riding upon it to enter another dimension…My sci-fi novel is called: “TIME TRIP ON A MOEBIUS STRIP.” What my main character finds when he enters this other dimension are 16 lost famous people of history, as well as an angel that all these people have already seen except two of them….You will find many interesting facts and links that these lost people seem to share amoung themselves, which I was amazed to discover when I read their biographies….There is much more to the novel than this which you will find while reading it…
Also, if you visit my blog at: MoebiusTripper.blogspot.com you will see many Moebius strip sculptues and some Moebius strip videos and a sample page from my sci-fi novel, etc…

2. MoebiusTripper,

Thanks for writing and congratulations on writing your novel. Your site does have a lot of interesting stuff. Definitely worth check out for whoever is reading this comment.

3. The first novel is made by Isaac Asimov, it is the history of a ghost train.

4. I think you are referring to a short story called:”Beluthahatchie” by Andy Duncan (1997) in a collection of short stories in Isaac Asimov’s “Halloween.”
Synopsis: A man named John rides on a train to Hell but refuses to get off. He ends up in the desolate town of Beluthahatchie.

Review: Another man vs. devil story only this time there is no clear resolution; nor any clear conflict for that matter. John is a Blues player whose songs of rebellion are revered in Hell. But is he the savior he is made out to be?

5. I do not know because in Italy the books are different.

Synopsis: a man investigate a lost train but he hear the sound. He discover that the complex rails of the city create a Moebius ring.

6. OK, I know the short story you are talking about…It is called “A Subway called Mobius,” by A.J. Deutsch…The story is in a book called: “The Omnibus Of Science Fiction.” The short story was even made into a movie in South America…I have not seen the movie yet, but will try to get a copy from Amazon…

7. The movie was made in Argentina…and if you go to: http://www.ram.org/ramblings/movies/moebius.html you will see the review of this film

8. Also, if you go to: http://www.dm.unibo.it/bologna2000/mosquera.html you will find out how the film was made and why.