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Author Topic: Nested Klein Bottles  (Read 853 times)

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Offline BlissTopic starter


Offline Paradox

Re: Nested Klein Bottles
« Reply #1 on: September 03, 2008, 10:18:30 AM »
I didn't sleep much last night, so maybe my brain isn't processing this as well as it should. How did they make one, if it can't be properly constructed in three dimensions?

Offline BlissTopic starter

Re: Nested Klein Bottles
« Reply #2 on: September 03, 2008, 10:37:26 AM »
I'm not entirely sure; they seem to work on the same principle as a moebius strip.

Offline Paradox

Re: Nested Klein Bottles
« Reply #3 on: September 03, 2008, 10:52:02 AM »


Mk. I did a quick bit of research on it, and it makes a lot more sense now. Three of them together! That's incredible.

Offline Revolverman

Re: Nested Klein Bottles
« Reply #4 on: September 12, 2008, 04:29:39 AM »
i've never understood whats so special about them, it looks like a wine bottle that comes with a handle.

Offline BlissTopic starter

Re: Nested Klein Bottles
« Reply #5 on: September 12, 2008, 06:28:08 AM »
If you can imagine putting your finger on any one point on the outside, and tracing it all the way up over the curve of the handle and following it down in... and then continuing one, your finger will trace upward inside the bottle, then inside the handle downward to come out the opening in the bottom, and back up to the spot where you first touched the bottle.

Like a Moebius Strip, the Klein Bottle is a shape that only has one side, even though it has an inside and an outside - it's all one surface.

Offline Revolverman

Re: Nested Klein Bottles
« Reply #6 on: September 12, 2008, 06:39:41 AM »
I can see why I failed advance math, im totally confused.

Offline Oniya

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Re: Nested Klein Bottles
« Reply #7 on: September 12, 2008, 08:41:56 AM »
I didn't sleep much last night, so maybe my brain isn't processing this as well as it should. How did they make one, if it can't be properly constructed in three dimensions?

To 'properly' construct a Klein bottle, the 'handle' part of it would not actually intersect the side of the bottle.  It would have to go 'up' into a fourth spacial dimension then 'down' into the interior of the bottle.  The way these are constructed, there's an edge where the bottle perforates itself.

As for how to make one:

A mathematician named Klein
Though the Moebius strip was divine.
Said he, "If you glue
The edges of two,
You get a weird bottle like mine!"