Understanding the Topology of Klein Bottles and Mobius Strips

[shankarvn]

Hi
Does anyone know what a klein bottle and mobius strip is ??what does embedding a surface in R4 mean??Is there any easy way to understand this??..Can someone enlighten me on this??I have an engg background..So please explain in simple language..
Bye
Shankar

 

[MiGUi]

Math define an orientable object as a surface that can be determined by a normal vector. Möbius strip don't verifies this, since you begin to walk in a point A upwards, and when we reach A again we are downwards, so there are two normal vectors at the same point for that surface, so... that means Möbius strip is not orientable. That can explain Klein's bottle as well, I think.

 

[matt grime]

You can make a mobius strip: take a rectangular strip of paper and glue together the two small ends and you get a loop. If instead you were to twist the paper by one half rotation before gluing you'd get a mobius strip.

A klein bottle is harder to make, indeed, properly it is impossible in the real world.

To make one you'd need to get two mobius strips and glue them together along their edge.

Note each mobius strip only has one edge.

I'll write some more in after I've finished teaching.

 

[Gokul43201]

http://mathworld.wolfram.com/MoebiusStrip.html
http://mathworld.wolfram.com/KleinBottle.html

 

[shankarvn]

Thanks a lot. that gives me a good picture..
Shankar