Monday, February 20, 2006

Disoriented?

Just to have fun with orientation, try making a Moebius strip. If you have a normal rectangular strip of paper, you can join one short end to the other to make a simple closed strip. IF you twist one end (by 180 degrees) first before joining with the other end, you have a Moebius Strip. The ants in the picture are actually on the same side of the strip, even though they appear to be on two sides. An ordinary strip has two sides (an inside and an outside), but a Moebius strip has only one side!

Think about that! :)

Take the normal rectangular strip and join the long ends to make a long cylinder. Just as in the case of the rectangular strip above, close the circles in the two ends of the cylinder in a simple way to make a hollow doughnut (a torus). What is the analogue of the Moebius Strip for the long cylinder? It is a Klein Bottle! A hollow doughnut has an inside and an outside, but a Klein Bottle does not. So it cannot hold any water as inside is also outside :P



Caveat: Klein Bottle does not physically exist in 3-dimensions (but in 4 dimensions!), so the picture is an illusion. I don't want you to get all cross-eyed looking at it. :P

2 comments:

Sowmya said...

Very interesting. Klein Bottle huh!! Knew about the moebius strip but not the klein bottle. Still thinking about your teaser!

bharath said...

as I say in the teaser you need the fourth dimension. If you see why? then you get the rough construction or the analogy. :)

yep, there is a lot of stuff like.