Möbius strip
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The Möbius strip or Möbius band is a geometrical object. It only has one surface. It can be made by using a strip of paper, which is twisted at the end. In Euclidean geometry there are two different strips. One turned left, and the other turned right.
There is another one topological object with the characteristics of a Möbius strip (a Möbius loop), created by Victor Gulchenko. The figure is a one-sided surface. It appears that the object has two closed contours. But actually those contours consist of one single closed two-dimensional contour. The following correlation can be observed in the case of this figure: two seemingly closed three-dimensional objects effectively consist of one two-dimensional surface.
Creation of the object:
1) Take a square sheet of paper (with the corners “A”, “B”, “C” and “D”). Extend each of the four corners with rectangular strips
2) The opposite corner strips of the sheet must be connected to each other (“A” with “C”; “B” with “D”)
3) With the A-C pair one of the two corner strips is given a half twist in a clockwise direction before being connected. With the B-D pair one of the two corner strips is given a half twist in a counter-clockwise direction before being connected
4) After the clockwise half twist, the “A” and “C” corner strips are glued together from the front side of the square. After the counter-clockwise half twist, the other two corner strips (“B” and “D”) are glued together from the reverse side
[change] Other websites
- Möbius strip at cut-the-knot
- Knitted version
- h2g2 - The Amazing Möbius Strip