Long ago, I saw a T-V presentation, either on "Mr. Wizard", or Doctor Dan Q. Posin, showing how a simple strip of paper may be made to do unbelievable things. Take a sheet of paper, like 8-1/2 X 11, and cut a strip off along on long side about 1-inch wide. Tape the ends together to form a cylinder 1-inch wide by about 4" diameter. Pierce the strip anywhere midway between it's edges with the point of a scissor, and proceed to cut along the center, all around, until you have separated the two pieces. Two cylinders, each 1/2 as wide as the original. Do this again, except, when bringing the ends of the strip together, twist the strip one one-half turn before taping the ends together. Now, proceed as before, piercing the center of the strip of paper with your scissor, and carefully cut along the center until you get back to where you started. Guess what? 2 pieces? NOPE! One single strip, now twice as long as the original! The strip of paper formed by twisting it 1/2 turn as we did, is called a "Moebius" strip. Take this new twice as long strip, and pierce it 1/3 of the way from one edge, start cutting it lengthwise, and you will marvel that the scissor-cuts pass one another and when finally finished, wind up at the starting point, with a most-unexpected result! This is all difficult to describe in words. I'll try to find a descriptive video. Meanwhile, if you can follow my description, try cutting a few connected at the ends ribbons in half, rolled up, and twisted then rolled up. You won't believe the results!
Here is a Moebius strip of paper. If you start anywhere along it's surface, with a pencil point, say, and trace all the way around, you will see that you have traced about BOTH sides of the strip! Impossible? Nope! August Ferdinand Mobius "Cutting a Möbius strip along the center line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip. This happens because the original strip only has one edge that is twice as long as the original strip. Cutting creates a second independent edge, half of which was on each side of the scissors. Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists." These descriptions I just found are no doubt better than mine. Look it over if yer of a penchant of weird newe stuff, like me! https://en.wikipedia.org/wiki/Möbius_strip