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The Klein Bottle

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The Klein Bottle is a surface on which you can move from outside to inside without crossing an edge. This shows that inside and outside are not universal concepts. In this movie Klein's Bottle is constructed by gluing an rectangle along the edges. Then the bottle is cut up again to yield a Moebius-strip.This Video was produces for a topology seminar at the Leibniz Universitaet Hannover. http://www-ifm.math.uni-hannov...

Channel: Howto & Style
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer

Length: 01:23
Rating: 4.52
Views: 136190

Tags: advent  bothmer  bottle  calendar  cg  fugru  geometry  glue  klein  mathematics  moebius  strip  topology  

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Video Comments

seeaeytch (November 30, 1999 at 12:00 am)
there's nothing special about this bottle at all. a cup has one hole and a bunch of space surrounded by plastic. so the entrance is the exit is just double talk for making a hole in a cup seem like it's some paradox.
jefforysanders (November 30, 1999 at 12:00 am)
exact same thing in any dimension. yo denial isnt just a long river in africa. what you had mentioned earlier about how it would be floating in the air was a good one! and how the air would be shooting out... lol you got it all figured out, it's obvious.5th dimension ownz buy their albums! :)
iownallnoobs (November 30, 1999 at 12:00 am)
lol... one is 3d, one is 4d? understand?
alcari (November 30, 1999 at 12:00 am)
Oh, to add...You can buy 3D mockup, or projections, of Klein bottles in some places, but they're not actual Klein bottles, because they do intersect themselves.It still doesn't have a real inside, but because it intersects itself, you can put water "in" it. sorry, that's where the mobius belt comparison breaks down. It takes a little more then 500 chars to explain all the math behind it.
alcari (November 30, 1999 at 12:00 am)
Well, no.It's hard to think in 4D, so lets use a 2D object in 3D space, the mobious belt.You can actually make a mobius belt, so do it now (or imagine one). Now, paint the left side of it white, and the right one black. You can't, because there are is no left or right side to paint. It's the same for a Klein bottle.You can't put anything inside a Klein bottle, because there is no inside.
KipSP (November 30, 1999 at 12:00 am)
looks like 1 hell of a bong!
jefforysanders (November 30, 1999 at 12:00 am)
can you please explain how they are not identical?
iownallnoobs (November 30, 1999 at 12:00 am)
the version you are referring is a real 3d version but its not a real 4d version.
jefforysanders (November 30, 1999 at 12:00 am)
obviously its real and exactly the same. whether you accept or deny it, has no influence on its existence. you may choose not to believe something exists when it truly does if you prefer. however, that klein bottle relies not on your belief nor lack of belief for its qualification of existence.
iownallnoobs (November 30, 1999 at 12:00 am)
that isnt a real klein bottle, a klein bottle is a 4d object where the entrance is also the exit which isnt true int he video you are talking about.

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