One of my goals with these science videos is to provide support to the homeschool community. After years of writing the Experiment of the Week, and presenting science shows for homeschool groups, I have been impressed with how strongly homeschool families are involved with hands-on science. I have also seen the need for a science curriculum that fulfills their educational needs. Starting with these videos, I hope to offer the homeschool community some of the science education support that they need, as well as a fun way to get students involved with scientific discovery.
I also try to use activities that involve common items. Most homeschoolers don't have access to test tubes, flasks, chemicals, microscopes and other scientific equipment. In the future, I hope to be able to guide them to inexpensive sources for science equipment to enrich their science curriculum.
This experiment seems simple, but the more you play with it, the more surprises you will discover. Using simple strips of paper, we will explore the science of Topology, the study of surfaces and spaces.
For this experiment, you will need:
- scissors
- paper
- tape
- a pen
Use the scissors to cut 2 strips of paper about 11 inches long and 2 inches wide. Lay both strips on the table and print the letter “A” at both ends of each strip. Then turn the strips over, with the A side down, and print the letter “B” at both ends of each strip.
Pick one of the strips to start with. Bring the ends together to make a circle, matching A to A, and tape the ends together. Pick a starting point on the inside of the strip and use the pen to draw a line down the center of the strip. Continue until the line connects with itself and you have a circle all the way around the inside of the strip. OK, no surprises there.
Now, we will do the same thing with the other strip, but this time twist one end, so that the "A" on one end matches up with the "B" on the other. Now, you should have a loop that is twisted in the middle. Use some tape to fasten the two ends together.
Once again, use the pen to draw a line down the middle of the strip. Keep drawing until the line connects back to itself. Do you notice anything unusual this time? By the time the line connects, you have drawn on both sides of the strip, inside and out. The Mobius strip really has only one side! The inside is part of the outside.
Not only does it only have one side, it also only has one edge. Pick a starting place on one edge. Use the pen to draw a line along the edge. Keep following the edge until you get back to your starting point. You will have a line along both edges of the strip, because they are part of the same edge.
For the next bit of strangeness, we are going to use the scissors to cut each strip in half. Don't cut through the strip. Instead, we are going to cut along the line that we drew down the center.
When you cut the first strip, you wind up with two separate loops. Again, no surprise there. What happens when you cut the Mobius strip? You get one big loop, with a twist in it. Why?.
Understanding the Science
Well, remember that the Mobius strip only had one edge, but that edge was twice as long as the strip, going down the left and the right part of the strip. When you cut it down the middle, you give it a second edge. Both halves of your cut are again part of that second edge, so it is also twice as long as the strip. That gives you a loop twice as long as the original strip, which has two edges. It is no longer a Mobius strip. If you draw a line down its center, you will see that this larger loop actually does have two sides and two edges.
For even more strangeness, cut that loop in half again. What did you get this time? You’ll have to try it to see. You can keep exploring with different variations. Try making your original cut near one edge instead of in the middle. Try give the original strip 3 twists instead of one.
Do Mobius strips have any uses? They sure do. Often, conveyor belts are Mobius strips, so the wear and tear is distributed over the entire surface, making them last longer. Typewriter ribbons (remember those?) were Mobius strips, letting them get more use from the ribbon. They are also used in continuous loop tape recordings, letting you use a shorter tape and get twice as much recording from it. If only someone would invent Mobius ice cream, so you could fit twice as much in your bowl.
Have a wonder-filled week.
