The Mobius strip is a simple but amazing thing. You can make it in a couple of seconds, and the surprises, patterns and properties of this phenomenon - a lot. To make this easier to understand in practice, take an ordinary strip of paper, glue, connect its ends. But it is imperative that one end is turned upside down relative to the other by half a turn. Well, the famous Mobius strip is ready.
One can talk endlessly about the resulting mysterious surface. Ask yourself how many surfaces the paper ring has. Two? And here is no - one. Check it out is very simple. Take a felt-tip pen or pencil and try to paint over one of the sides of the tape, without tearing off and without switching to the other side. Happened? And where is the unpainted side? That's it ...
The name of the tape was given by its inventor: August Ferdinand Mebius, professor at the University of Leipzig. He devoted his long and fruitful life to scientific work (and this is 78 years), and he kept his mind clear until his departure. At 75 years old, the professor described the unique properties of a one-sided surface with an apparent bilayer. Since then, the best minds of geometry, physics, and even spirituality have explored this object up and down.
You yourself can conduct several experiments by picking up the Mobius strip. Try to cut it along, having previously drawn the middle line over the entire surface. What do you think will happen? Two rings of smaller width? Again wrong - one thing! Twice as long as the previous one, but twisted twice already. So he will already have two surfaces, and not one, as in the first case. This curl is called the Afghan ribbon, it is also widely known to researchers. By the way, in spirituality this effect is called a symbol of duality and is interpreted as an illusory perception of the one.
And if you again draw a longitudinal line, but not in the middle, but closer to the edge by a third of the width of the tape? Cut the resulting ring, and you will already have two in your hands: the Mobius strip and the Afghan ribbon, and in an incomprehensible way they will be linked together.
But these are far from all surprises. When gluing the tape into a ring, try to take not one, but two paper strips. And then three or even four. I guarantee: the result will surprise you even more!
An interesting experiment can be put hypothetically. Taking a double Mobius strip (that is, glued from two strips) and sticking a finger between them (pencil, wooden stick - whatever), we can drive them between the ribbons endlessly, thereby proving that the figure consists of two separate parts. Now imagine a fly creeping between these tapes. The lower strip for her will be the "floor", the upper - the "ceiling", and so on to infinity.
But in reality, everything is not at all as simple as it seems. After all, if you put a mark on the beginning of the fly’s journey “on the floor”, then when the insect makes a circle, this very mark will already be “on the ceiling”. And in order to go “to the floor” again, it will be necessary to complete one more round.
Imagine a fly crawling along a street. To her right are houses under even numbers, and to her left, respectively, under odd numbers. Taking a walk, at some point, our traveler will be surprised to notice that the odd numbers are already on the right, and the even numbers are on the left! It’s scary to imagine such a situation on our real right-hand drive roads, because soon you will have to face other “head-to-head” strollers. Here it is - Mobius strip ...
The application of this and other laws was found not only in a hypothetical, but also in real life. For example, belts are created on the basis of the tape in printing devices, automatic transmission, an abrasive ring in sharpening mechanisms and much more, which you do not even suspect. Truly, the Mobius strip is a mystery that can be studied indefinitely!