13 January 2006

[42+1] Klein Bottle – No Relation

How would you like to have your very own 3D immersion of a 2D non-orientable manifold that can only truly be represented in 4 Dimensions?

What I speak of, of course, is the Klein Bottle. I have an affinity for all things Klein, and the Klein Bottle is amongst the coolest things I've found.

Now, all that high-talk in the first paragraph was just a way of saying a bottle with one side (take a good look at the accompanying picture, and let your eye travel about on it). In the same way that a Möbius strip is is a one-sided surface, a Klein bottle is a one-sided volume. It has only one side; or, looked at another way, its outside contains its inside. This, by the way, is what they mean by "non-orientable", which is another way of saying you can't say whether you're inside it or outside it.

The difference between 3D and 4D space is, of course, that in 3D space there is a hole in the side where the spot can come through and then be mated to the base. In 4D space the bottle's side is pierced by the spout but is still intact.

It's topology, so that's about the limit of my understanding too.

But the reason I told you all that is to tell you this: there's actually a company, Acme Klein Bottles, that makes and sells them. You can find 'em all there; classic Kleins, Erlenmeyer Kleins, even Klein Steins (which you may or may not be able to drink from). Prices range from $30 (for the small classics) to $12,000 (for huge Kleins for people with much more money than sanity.

Visit them...you must! It's a hoot!

(Illustration is copyright Acme Klein Bottles)


stan said...

The jigsaw puzzles are my favorite.

Samuel John Klein Portlandiensis said...

How cool! Do you have any of them or have you just seen them?

I may try to inveigle The Wife™ into getting us some of that stuff.

stan said...

I just saw them on the site. They're the funniest thing on there.