Can any of you math wizards explain the concept of a mobius strip.?

A mathematician confided

That the Mobius band is one-sided

And you'll get quite a laugh

If you cut one in half

'Cause it stays in one piece when divided.

-Cyril Kornbluth

Definitely make one for yourself, then just play with it. Try cutting it in different ways. Try picking a point then drawing a line on only one side. Be shocked and awed when there is no "one side" then cut along the line.

it is a one sided piece of paper because the twist in the paper means that you can write a line, without crossing an edge, that covers the entire paper. Or an ant could walk everywhere on its surface without crossing an edge.

Normally, you have to cross an edge to get to the 'other side', but not a piece of paper that has a half twist - or any odd number of twists - and is 'connected'. Of course, we only tape or glue the paper to simulate that with paper.

It would not be easy to actually make a continuous strip of paper in that shape! But one could stamp them out of plastic or glass.

Its complete 'two dimensions in three dimensional form' called a Kleins bottle has been made. That is a sort of a mobius strip in every direction. i t is a bottle with no inside or outside. Just ONE side. You can find a picture at

http://en.wikipedia.org/wiki/Klein_bottle

Make one out of paper by taking a strip one-inch wide by 11 inches long. Take and twist and make the top of the front meet the bottom of the back. Tape together and you have made a Möbius Strip.

To show that you now have a one-sided figure, put a pen on the strip and draw a continuous line without lifting your pen from the paper. It will take two "revolutions" of the manifold to complete the path. You will find you have marked both "sides" of this one sided figure.

Another way to think of it on a plane: ever play video games? What happens when you fly past one edge of the screen, you just wrap-around and remain within the Möbius space. Same thing here, it just has a name.

A möbius strip is an example of an interesting phenomenon of topology. It has only 1 side, and one edge. If you take a long strip of paper, and attach one end to the other to make a circle, then twist it one half time before fixing it in place with tape, you will your own möbius band.

To experiment: draw a line along the middle of the strip, and continue until you meet where you started off. You have drawn on both outside and inside. You will notice that there is only one side to draw on!

Now cut along the line. The result will be not two thinner strips, but one. Try it.

If you do this cutting procedure at one third from the side, instead of directly in the middle, you will get two interconnected loops.

The fun is endless.

A mobius strip has only one continuous edge -- which sometimes seems to be on the inside and sometimes on the outside of this three dimensional shape. It is a three dimensional shape with only "one side."

Try making one with a strip of paper. Make one twist in the strip before gluing together the ends. Trace the "one side" with your finger. The one side is both inside and outside!

It's a structure has only one side. Like a Klein bottle.

sorry...i'm not specialist in mathemathic problem..