Möbius tape - an endless mystery of our time

Mobius tape is a simple, but amazing piece. You can make it in a couple of seconds, and surprises, regularities and properties for this phenomenon - a lot. To make this more understandable in practice, take a regular strip of paper, glue, connect its ends. But it is imperative that one end is turned in relation to the other half a turn. So the famous Mobius ribbon is ready.

On the resulting mysterious surface you can talk endlessly. Ask yourself the question of how many surfaces have a paper ring. Two? But there it is - one. Check it out very simply. Take a felt-tip pen or pencil and try to paint one side of the tape, without tearing off or passing to the other side. Happened? And where is the unpainted side? That's what it is ...

The name of the tape was given by its inventor: Augustus Ferdinand Möbius, professor at the University of Leipzig. He devoted his long and fruitful life to scientific work (which is 78 years old), but he kept his mind clear until his departure. In his 75 years, the professor described the unique properties of a one-sided surface with an apparent double layer. Since then, the best minds of geometry, physics and even spirituality have explored this object along and across.

You yourself can conduct several experiments, picking up the Mobius band. Try cutting it along, after having preliminarily centered the entire surface. What do you think will happen? Two rings of smaller width? Again it is wrong - one! Twice as long as the previous one, but twisted twice already. Here he has something already will be 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 single.

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 received ring, and in your hands there will be already two: the Moebius tape and the Afghan tape, and in an incomprehensible way they will be linked to each other.

But this is not all surprises. Try to glue the tape in the ring to take not one but two paper strips. And then three or even four. I guarantee: the result will surprise you even more!

A curious experience can be put hypothetically. Taking a double Moebius tape (that is, glued from two strips) and sticking a finger between them (a pencil, a wooden stick - anything), we can drive them between the tapes endlessly, thus proving that the figure consists of two separate parts. And now imagine that a fly creeps between these ribbons. The lower strip for her will be "floor", the upper one - "ceiling", and so on ad infinitum.

But in reality everything is not so simple as it seems. After all, if you put the mark of 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 to go back to the floor again, you will have to make another circle.

Imagine that the fly is crawling along the street. To the right of her are houses under even numbers, and on the left, respectively, under odd numbers. Making a walk, at some point our traveler is surprised to notice that odd numbers are already on the right, and even - on the left! It's scary to imagine such a situation on our real roads with right-hand traffic, as soon we will have to face other walking "foreheads." That's how it is - Mobius tape ...

The application of this and other regularities was found not only in hypothetical, but also in real life. For example, on the basis of a tape belts in printing devices, automatic transfer, an abrasive ring in sharpening mechanisms and many other things about what you at all do not suspect are created. Truly, the Mobius tape is a mystery that can be studied indefinitely!