how many M&Ms can you fit inside a Kline bottle?

[Guy Fawkes]

no cheating!

[Rabrrrrrr]

1. e^(-jPI)

[trof]

2. What's a Kline Bottle?

[edbermac]

3. Klein Bottles...

Don't ask me what they're used for...

[redqueen]

4. reducing, separating, etc... right?

[mcscajun]

5. They are critical for every "Mad Scientist" movie ever made.

:)

[Rabrrrrrr]

9. No, you don't get them in movies. Those are Erlinmyer flasks

and other laboratory bottles.

Klein bottles are purely mathematical constructs, in which the outside and the inside have no separate distinction.

You can buy glass ones - like the ones shown in the other post - but they aren't true Klein bottles, since they're three-dimensional.

http://en.wikipedia.org/wiki/Klein_bottle

In mathematics, the Klein bottle is a certain genus-1 non-orientable surface, i.e. a surface (a two-dimensional topological space), for which there is no distinction between the "inside" and the "outside" of the surface. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is closely related to the Möbius strip and embeddings of the real projective plane such as Boy's surface.

Picture a bottle with a hole in the bottom. Now extend the neck. Curve the neck back on itself, insert it through the side of the bottle (a true Klein bottle in four dimensions would not require this step, but it is necessary when representing it in three-dimensional Euclidean space), and connect it to the hole in the bottom.

Unlike a drinking glass, this object has no "rim" where the surface stops abruptly. Unlike a balloon, a fly can go from the outside to the inside without passing through the surface (so there isn't really an "outside" and "inside").



And a lot more.

hence my first post about the number of M&Ms in which I said e^(-jPI)

(and you can tell I'm an electrical engineer since I used j and not i :-) )

Though the real answer is all marbles in existence, and there's still room for the rest of all existence.

[mcscajun]

11. My mistake — I went by the pic in the later post, not the Klein in the OP

And — I didn't look CLOSELY ENOUGH at the bottles, either.

:shrug:

So, a Klein bottle is pretty much a 3-dimensional moebius strip :P

[slutticus]

12. Those aren't real

Klein bottles can't exist in 3D space.

They are like a multi-dimentional version of a Mobius strip.

[Guy Fawkes]

7. whatever is inside is outside, and whatever is outside is inside..

and then your brain implodes from thinking about this.

[Born in the Maze]

6. How many do you have?

They're all inside already!

[Speck Tater]

8. An infinte number because

since inside = outside, the Klein bottle can be thought of as containing the entire universe.

[Salviati]

10. or alternatively zero, since they're all outside...

[mcscajun]

13. I like this one better...from a reply by Rabrrrrrr

"Though the real answer is all marbles in existence, and there's still room for the rest of all existence."