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More 4-Dimension Objects: The Klein Bottle

This is a Klein Bottle: a 4-D object that is `non-orientable.` It is to 4-D what a Mobius Strip is to 3-D.

submitted by: MacGuffin
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More 4-Dimension Objects: The Klein Bottle. This is a Klein Bottle: a 4-D object that is `non-orientable.` It is to 4-D what a Mobius Strip is to 3-D.
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Hits: 8315 | Favorites: 2 | Emailed: 1 | Rating: 1.7 | Category: Science | Date: 07/18/2012
 
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doug1963aaa
Male, 40-49, Southern US
 347 Posts
Sunday, July 22, 2012 6:54:28 PM
@MacGuffin: I have written software that allows one to visualise true 4-d objects in 3-d using 3-d glasses. I have spent a good amount of time over the last 30 years working on it, and I have gained a solid understanding of 4-d geometry in the process.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Saturday, July 21, 2012 1:37:12 PM

>>>@MacGuffin: I don't know why you keep insisting that Klein bottles are 4D objects when they are clearly NOT.

...

Hell, you can *buy* Klein bottles!
http://www.kleinbottle.com/ <<<


Well, if you can *buy* 3D projections of the real thing on the internet and everything, that *must* prove that the 4D object that said 3D projection is a projection of can`t exist.

Read this, then realise how mistaken you are. To quote:

"While the Möbius strip can be embedded in three-dimensional Euclidean space R3, the Klein bottle cannot. It can be embedded in R4, however."

As I said, this *is* a 3D projection of such an embedding in R4 - that`s how the object is shown to pass through itself. That only happens in 4D.

MacGuffin
Female, 30-39, Europe
 2597 Posts
Saturday, July 21, 2012 1:26:05 PM

@MacGuffin--a 4-d Klein Surface would not show an intersection and would rotate without any flattening.

This is a matter of some expertise for me.


Again, this is a *3D projection* of a 4D Klein Bottle. Nobody is saying that it is the 4D object itself. If it was, we'd be unable to perceive it, since we live in 3D.

I guess it`s not that much of an area of expertise for you, or you`d be able to understand that simple concept.

HiEv
Male, 40-49, Eastern US
 454 Posts
Saturday, July 21, 2012 4:17:13 AM
@MacGuffin: I don't know why you keep insisting that Klein bottles are 4D objects when they are clearly NOT.

Seriously, no part of a Klein bottle needs to project into the 4th dimension for it to be a Klein bottle, therefore it is, by definition, *not* a 4D object.

Hell, you can *buy* Klein bottles!
http://www.kleinbottle.com/

Since we cannot build 4D objects, doesn`t that prove to you that they`re *not* 4D?!?

(Or do you have some strange definition of 4D that most of us don`t use?)

Squrlz4Sale
Male, 40-49, Eastern US
 6018 Posts
Thursday, July 19, 2012 11:14:49 PM
Yeah, I uhhh... have *no* idea what's going on here.

~looks for this thread`s exit~

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