Mobius Strip: Twist It!

Mobius Strip: Twist It!

Sometimes it is not easy to predict what will happen when you start cutting.

Materials

• Rectangular paper, like notebook paper or typing paper
• Tape
• Scissors
• Pencil

Instructions

• Cut four long, thin strips from the paper, each about an inch-and-a-half wide
• Mark the ends of each strip A and B on one side and C and D on the other side so that A and C are at one end and B and D are at the other
• Overlap and tape the ends of the first strip to each other, so that A overlaps B. Mark it with a 0, for 0 twists
• Overlap and tape the ends of the second strip, but, just before you connect them, twist one end of the strip so that A overlaps D and then tape the ends to each other. Mark it with a 1, for 1 twist
• Optional: Twist one end of a strip twice so that A overlaps B and tape the ends to each other. Mark it with a 2, for 2 twists
• Optional: Twist one end of a strip three times so that A overlaps D and tape the ends to each other, marking it with a 3 for 3 twists
• Optional: Cut each of the long loops in half, along the long end

What Should Happen?

For the first strip, you will get a single loop. A loop has an inside and an outside. You can draw a line along the length on one side and on the other side. The lines will not overlap with each other. They will be two separate lines, one on the inside of the loop and one on the outside.

For the second strip, with one half twist, you will get a Mobius strip. It is known by the fact that, unlike the first loop, it only has one side. There is no inside and outside of the loop. If you draw a line along the length on one side, it will continue until you meet up with the beginning of the line.

Optional:

The third strip, with two half-twists, also has an inside and outside and the fourth strip, with three half-twists again only has one side.

Optional:

• The first strip, with zero half-twists, when cut in half, will give you two separate loops, half as wide as the first one.
• The second strip, with one half-twist, when cut in half, will give you one strip twice as long as the first one, with two full twists in it. Now, if you draw a line along the length of the strip on the inside or outside, you will get separate lines.
• The third strip, with two half-twists, will give you two interlocking strips when you cut it in half.
• The fourth strip, with three half-twists, will give you a single loop with six full twists
• An even number of half-twists yields linked strips, each with the same number of twists as the original
• An odd number of half-twists yields a longer strip with twice as many full twists as the original had half-twists

Why Is This Useful?

Mobius strips have been used as conveyor belts to even the wear of the belt.

They have been used in recording tapes, to double the playing time and in fabric computer printer and typewriter ribbons because they can be twice as wide as the print head and use both halves evenly.

Dutch graphic artist M.C. Escher incorporated topology, the study of shapes and spaces, a mathematical discipline of which the Mobius strip is a part, in his art. He made it appear in his work, Relativity, for instance, that a walker could never climb to the top of a set of stairs.

Thanks to highlightskids.com for their description of the paper twist.

 

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers”

http://newgrandmas.com

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