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Mystery Twist


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Starring

You and Your Students!

Script By

Vicki Cobb, Education World Science Editor

Synopsis

Explore a mathematical mystery by using strips of newspaper to design experiments.

Genre

  • Topology (Mathematics)

Required Props

  • lots of large-sheet newspapers
  • paper cutter
  • scissors (ideally one scissor per student)
  • transparent tape (for student use)

Show-Biz Science is scripted by popular children's book writer Vicki Cobb. Click to learn more about Vicki or to read a brief synopsis of her philosophy of teaching science.

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Setting the Scene (Background)

As a scientist, I love mysteries! I can live without knowing all the answers. I think it's fun and interesting to come across something I don't understand and experiment with it.

There is a branch of mathematics, called topology, which is the study of what happens when a surface is twisted or distorted. That's what this experiment is all about. Don't be intimidated by that! This activity will give you a chance to create a level playing field with your students while having a lot of fun. I do this experiment with parents and children during an evening of science fun and it is always a smash hit!

Stage Direction

Use a paper cutter to prepare 3-inch wide strips of paper ahead of time. I use the large-format newspapers (like the NY Times) and cut strips parallel to the words with the fold in the middle. This creates strips about 26 inches long and 3 inches wide. Have transparent tape and scissors available for your students.

Plot

Act I
Bet you can't make two loops out of one! Bring the two ends of a newspaper strip together to make a loop. Before taping the two ends of the strip together, turn over one end of the strip to make a twist. Then tape. Make sure the tape goes all the way across the end of the strip.

Now try and cut the loop into two loops by cutting down the center of the strip lengthwise. Surprise -- you get one long loop twice as long as the original with two twists!

Act II
You can make two loops if you start cutting in a different spot! This time start cutting the strip one-third the distance from the edge (instead of the half-way point). Keep on cutting around the strip, keeping the same distance from the edge...

Ta da! The resulting figure is a loop twice as long as the original but with a same-sized loop linked to it.

Act III
What happens when you try and cut a loop in half that has two twists in it? What happens when you cut this result in half? There are many experiments your students can do with these strips. Encourage them to be creative and keep on wondering.

Behind the Scenes

August Ferdinand Mbius (1790-1868) was a German mathematician who invented the strip bearing his name. The twist made the figure have only one side. You can prove that by drawing a line down the center of the loop without lifting your pencil until you meet your starting point. The line is continuous although it actually covers both sides of the paper.

The wonders of a Mbius strip have been immortalized in a poem:

A mathematician confided
That a Mbius strip is one-sided.
You'll get quite a laugh
If you cut it in half
For it stays in one piece when divided.

Article By Vicki Cobb
Education World®
Copyright © 2006 Education World

03/09/2006



 

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