"Möbius strip"
You can build a Moebius strip!
Material - An elongated rectangle of paper, with one side colored
- Tape
tape - Scissors
Procedure
1 Cut the elongated rectangle.
2 Draw on the white side, along a dashed line or dotted.
3 Build him a cylinder without caps, tape attaching the ends of the rectangle (as shown in Figure 1). 4
Imagine an ant walking leave the cylinder under the rule to move only along the dotted line, always in the same direction. In this case, just walk through the interior of the cylinder (or abroad, if the dotted line you left out). That is, the cylinder has an interior and exterior.
5 Carefully remove the tape adhesive and rejoins the ends together, making a turn before the rectangle (see Figures 2 and 3).
Explanation
What you have built is called "Möbius strip." In this case, the ant can not obey the rule set, first travel across the dotted line and, if they are forced to go forward, must begin to walk down the side without the dotted line, then resume the dotted line and so on. That is, the "Möbius strip" has only one side (no interior or exterior): such figures are called "figures without end."
August Ferdinand Möbius (1790-1868) was born in Schulpforta, Germany. He was a pupil of Gauss and worked as an astronomer and mathematician at the University of Leipzig. He was one of the pioneers of the topology, investigated the area where one-sided surfaces, such as his famous tape, discovered in 1858.
"Klein bottle"
The Klein bottle can not know what the face "inside" and what is the face of "outside" that figure is endless!
Want to see the Moebius strip and Klein bottle in 3-D?
http://www.luventicus.org/articulos/03GdA001/i.html
Christian Felix Klein was a German mathematician (1849 - 1925) with a passion for geometry. I think his famous bottle in 1882. Professor at the University of Gottingen (1886), was the founder of the "Encyclopedia of Mathematics" (1895) and one of the lawyers in the renewal of the teaching of mathematics in high school.
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