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As the applause dies down the magician readies her next trick. She picks up
a closed loop of string a meter in circumference and shows it to the audience
before letting it dangle from her left hand. Next, she lifts a solid metal ring
with her right hand and lets the spectators get a good look at it before she
brings it up around the dangling loop. She is careful not to let the ring touch
the string as she raises it to a point just below her left hand. With the magic
word, "abracadabra," she drops the ring. It falls and magically becomes knotted
to the bottom of the loop. Thunderous applause again fills the room at this
amazing trick. "How did this happen!" the audience wonders. The two objects
were not connected in any way before the magician dropped the ring; yet now
they are tied together in a knot. The magician notes the puzzled looks and wonders
if anyone in the audience suspects that the trick she has just performed is
nothing more than an application of mathematics. This thought quickly passes
as she realizes it's unlikely that the audience would equate magic and mathematics.
Her secret is safe. She picks up a magic wand and readies her next trick.
The event described above is not an illusion like the majority of magic tricks.
Instead, it is one of a small class of related tricks that applies principles
from the mathematical field of topology. Since this magic trick is not a "trick"
in the sense that it uses slight of hand or specially designed props to fool
the audience, I prefer to think of it as a mathematical puzzle. Therefore, it
is an apt subject for this month's Puzzle Corner.
The Stringing the Ring activity has two parts. The first part is fairly
simple and is designed to help students understand how the loop gets knotted
around the ring. Once students have done this, they have discovered the secret
to the puzzle and are ready for the second part, applying this knowledge to
the trick and performing it. This second part, which is illustrated on the sides
of the sheet, may entail some frustration. Even after students have discovered
what they have to do to get the ring knotted to the loop, they may not be successful
since a certain amount of skill is involved. Encourage students to keep trying
until they succeed. To extend this activity, have students experiment with some
of the variables - length of string, thickness of string, ring size, etc. --
to see if they can make the trick easier to perform. These explorations make
the activity much richer.
The materials needed for this puzzle are a piece of string or yarn and a metal ring. The string should be about one meter long with the ends tied to form a loop. The metal ring I have is 6 cm (2.5 inches) in diameter, but this dimension may not be critical. Rings like this can be found in craft or hardware stores. If solid rings are not available, chart rings or ring-like objects such as rolls of masking tape can be substituted; however, this may affect the ease of performing the trick. How many rings you will need depends on how you want to do the puzzle in your classroom. If you want everyone to work simultaneously, you will need one per person. Otherwise, you can provide fewer rings and have groups of students work on the puzzle or just a single ring and place it in your puzzle corner.
Worksheet
I hope you find this puzzle enjoyable. Because of the magic connection it has the potential to be quite popular. Once the trick is mastered, students will want to take this mathematical phenomenon home to show family and friends. I would like to thank AIMS National Leadership Network members Bill Jenner, Kay Kent, and Joe Itel for their great input on this activity. Puzzle Corner |
