What is the Moebius band and why it should be cut? That who knows what is a tape (sheet) of Mobius and in the childhood it glued
and cut, it will be pleasant to remember the surprise of that time from the received result and a pure feeling of Knowledge. They can pass this article and indulge in memoirs. Who did not cut - very I recommend. And connect children, it will be pleasant to them. Stock up with several sheets of usual white paper, glue and scissors.
We take the paper tape ABCD. We put its ends of AV and CD to each other and we stick together. But not anyhow, and so that the point And coincided with a point of D, and B point with a point S. Poluchim such overwound ring. Also we ask a question: how many the parties at this piece of paper? Two, how at any other? And anything similar. It has ONE party. You do not trust? You want - check: try to paint over this ring on the one hand . We paint, we do not come off, we do not come over to other side. We paint... Painted over? And where second, pure party? Is not present? Well-.
Now second question. What will be if to cut a usual sheet of paper? Of course, two usual sheets of paper. More precisely, two halves of a leaf. And what happens if to cut lengthways in the middle this ring (it and there is Mobius`s leaf, or the Moebius band) on all length? Two rings of half width? And anything similar. And what? I will not tell. Cut.
Cut? It`s cool. Now make a new leaf of Mobius and tell what will be if to cut it lengthways, but not in the middle, and is closer to one edge? The same? And anything similar. And if on three parts? Three tapes? And anything under... And so on. Investigate further this amazing (and nevertheless absolutely real) a unilateral surface, and you receive the sea of pleasure. And it differently calms the nerves upset with forum disputes, I assure you. What can be polzitelny Pure Knowledge?
Liszt Mobius - one of objects of field of mathematics under the name “ topology “ (in a different way - “ geometry of the provisions “) . Surprising properties of a leaf of Mobius - it has one edge, one party , - are not connected with its position in space, with concepts of distance, a corner and nevertheless have quite geometrical character. The topology is engaged in studying of such properties. In Euclidean space there are two types of strips of Mobius depending on the direction of twisting: right and left.
And it is possible to read in more detail in the fine book “ Magic two-horn “ Sergey Pavlovich Bobrov, chapter 8 . What book can be downloaded here (or here). Here only format of files there special: DjVu and what to do that to open it, is written here, and there is nothing difficult there. The eReader of the Deja vu is installed and opens these files in the format similar to the PDF format, only they are not such bulky. But with pictures! Though it is the book in general the nursery, but it at the same time not so simple, and is written very fine, vividly and fascinatingly. Children read it with ecstasy, and here it can appear the adult too hard! Therefore give, give it to children, certainly not kindergartners, and a class so in 6 - 7 - 8. But not later. It is the cheerful, kind book, and at the same time grandiose food for mind!
The Moebius band was found by the German mathematician Augustus Ferdinand Mobius in 1858 Augustus Ferdinand Mobius - German geometr, professor of the Leipzig university of the first half of the 19th century. To it was considered that any surface (for example, a sheet of paper) has two parties. Mobius made amazing discovery - received a surface which has only one party.
They say that Augustus Ferdinand Mobius when it watched the maid who put on a scarf a neck thought up the tape.
But the Moebius band not only exercise for reason, it also quite is practically applied. In the form of the Moebius band do a strip of the tape conveyor that allows it to work longer because all surface of a tape evenly wears out. The Moebius bands in systems of record on a continuous film (to double record time) are still applied, in matrix printers the painting tape also had an appearance of a leaf of Mobius for increase in an expiration date. And maybe, and still where - nibud.
The magnificent Moebius band was represented in a picture by Maurice Asher, inexhaustible on an invention.