Möbius strips are one of the wonders of the world of Maths.
They take their name from a German mathematician, August Möbius, who discovered them in 1858.
Their simplest version is a long paper strip, half-twisted and joined together at its ends.
What’s so special about them?
We all know that the main property of a surface is that it is orientable, that is, it has two sides. This means that we could draw two different figures on each surface, or paint each side with a different colour if we wanted to.
A Möbius strip, on the other hand, is a non-orientable surface, because it has one side only. And this is precisely what gives to it its peculiar properties.
Just imagine. If we started drawing a straight line from any point on its surface, after the first round we would indeed end up at the same starting point, but on the other side of the strip!!! To get back to the original starting point, we would have to continue drawing for another whole round…
But this is just the beginning.
What do you think would happen if you cut a Möbius strip along its length? Well, it depends. However, if you were sure to get TWO strips after cutting it, well, you’d be surprised!
If you cut it along the middle, in fact, what you get when you have finished is ONE long strip with a DOUBLE twist, so something totally different from the original Möbius strip, which only has one twist!
How can it be? Is it a kind of magic? 😉
Now imagine to cut the strip, let’s say, starting at one-third of its width: this time you would eventually get the TWO strips you were expecting, a big and a small strip. With a difference. The small strip would be another Möbius strip, with one twist only, while the bigger strip would be AGAIN a strip with two twists… and what’s more, BOTH STRIPS WOULD BE JOINED TOGETHER!
Don’t believe me? Watch this video before making yourself a Möbius strip and finding out about its incredible properties!