The following Moebius Strip variation was new to me. It was sent from Martin Gardner to mathematician Ivars Peterson in 2000. The model is easy to construct and what results from cutting it is surprising. Preparation: You’ll need to print out the figure in the PDF files.
You’ll also need a small pair of scissors and some Scotch tape.
1. After printing the PDF page, cut out the cross-shaped figure, cutting on the heavy black line.
2. Bring up the short arms of the cross and tape them together (Photo 1).
3. Bring up the long arms of the cross in the opposite direction. Give one end a single twist, and then tape the ends together (Photo 2).
Before you begin the following instructions, take a moment to imagine what the outcome will be. My guess is you’ll be surprised by the result.
Use the scissors to cut the twisted loop into thirds by cutting along the red line. Because of the twist, you will be looking at the back side of the paper at one point during the cutting. You should still be able to follow the red line.
Now cut the other loop in half, following the green line.
The paper emerges from this process in a little bit of a mess. Carefully untangle everything to see the surprising result.
For more interesting recreational mathematics information, take a look at Ivars Peterson’s