Fun with Science

Möbius Strips

When you cut a piece of paper in half, you usually get two smaller pieces of paper. Is there any way to cut the paper in half and still end up with just one piece?

What you'll need:

  • several sheets of construction paper
  • scissors
  • adhesive tape
  • markers
1. Take a piece of construction paper and cut a strip that measures about one inch wide and eleven inches long.  
2. Holding one end of the strip in each hand, twist one end and then tape the two ends together to form a loop. This is a single-twist loop.
3. Now, using scissors cut the loop lengthwise along the centerline. What do you end up with? Instead of making two separate loops, you have made one single loop that is longer than the original one!

4. Next, try making another paper loop. This time give one end two twists, and tape the ends together as before. This is a double-twist loop.

5. Now cut the loop along the centerline again. How does this one turn out? When cut, the loop with two twists becomes two loops that pass through each other.
How does this work? This happens because the twisted paper loop has only one side. You can test this by using a marker to draw a line down the center of the strip. The marker will cover all the surfaces of the paper and finally end up at the starting point. These twisted loops are called Möbius strips, and are named for a famous German mathematician in the nineteenth century who worked in a branch of mathematics known as topology.

Adapted from Paper Science, by Harry Milgrom (Walker and Company, New York, 1978) and Is Science Magic?, by Ovid K. Wong (Childrens Press, Chicago, 1989).

 

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