Monday, August 27, 2012

Montessori Moebius: Easy and Cheap Geometry

A Moebius Strip has no inside or outside.  

Here is a cheap and easy math demonstration you can do with your elementary kids.  All you need is:
  • one sheet of paper (it's nice to have something big, like easel paper or a newspaper)
  • scissors
  • tape or glue
  • pen, pencil or marker (best not to use a marker that bleeds through)

Step 1:  Cut a long, narrow strip of paper (about 2 inches wide).

Step 2:  Grasp each end of the strip and twist one end so that it is turned over (i.e., give it a half-turn).

Step 3:  Tape or glue the ends together flat.

Step 4:  Point out that what seems to be the inside of the loop becomes the outside, and vice versa.

Step 5:  Have the kids take a marker, pen or pencil and, starting in one spot of the strip, continue all the way around, until they meet back up with the starting point.  This proves that a Moebius strip really has only one side!

Step 6:  Pinch together one part of the strip and begin cutting to make a hole.  Then insert the scissors and cut all the way around the strip.  Shouldn't this cut the Moebius strip into two separate pieces?  No!  You just end up with a single strip that is twice as long.

Step 7:  EXTRA CREDIT -- If your new strip is wide enough, begin this process all over again.  You may find a nice surprise!  (Do you want a hint?  You should end up with two linked loops!)

For more info see this article.  They are not only interesting, they also have practical applications.  There are Moebius strips in the world around us--some typewriter ribbons and computer printer cartridges and some automotive belts are Mobius strips.  In both cases, the design allows for a more efficient belt or band. 

Montessori Monday

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