How Many M&M's Can Fit Inside a Klein Bottle?

1. beajerry
   January 27th, 2007 at 4:31 am

   Not a true Klein bottle.

2. MrPumpernickel
   January 27th, 2007 at 8:13 am

   Yes, that is a true klein bottle (you just cannot see where the "spout" goes through the bottle).

   However (and yes, this can be argued ad nauseum), the M&Ms aren't inside the bottle, nor are they outside. They're contained by the bottle yes, but since there is no true inside or outside saying that they're "in" the bottle is a bit backwards.

3. Ty
   January 27th, 2007 at 11:39 pm

   Is it a true klein bottle? or is it just the shadow of a true klein bottle, since klein bottles only exist in 4 dimensional space? i dunno

4. beajerry
   January 28th, 2007 at 5:45 am

   Well, even if you follow the link to the close-up pics, I still cannot see where the spout continues through the bottle, nor can I see where it merges with the bottle again.
   It just appears to be a simple bottle with a spout connected to one side.

5. Denita TwoDragons
   January 28th, 2007 at 5:47 pm

   What you don't see (because it's blocked by the M&Ms) is that that "spout" merges with the floor of the "bottle", flaring out to become the outer wall of the structure.

   A Klein bottle is basically what would happen if you stretched a moebius strip so that ALL sides are connected, not just the two end strips. Of course, a 3D model isn't a true realization, because the hole through which the "spout" passes is a "cheat"--a true Klein bottle would be one continuous, uninterrupted shape--but is necessary for the bottle to exist as a tangible, three-dimensional object.

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

   --TwoDragons

6. nex
   February 28th, 2007 at 5:04 am

   MrPumpernickel is wrong, it's not a true Klein Bottle because it intersects itself. Of course you have to imagine it as the shadow of a 4-dimensional object ...

   Now it's blindingly obvious that the candy is falling out left and right, as this insufficient surface can't possibly contain them. Alright, so it's not obvious. But picture a few points (drawn as dots all the same size) on a piece of paper, and surrounding them with one other dot. You get the idea.

   Beajerry is of course right, it _appears_ to be an ordinary bottle with the spout connected to the side. But if it really was, how in the world would they have gotten the M&Ms in? Huh? Huh?

   It's not too difficult to find pictures of unfilled bottles that let you see the entire topology, so I'll leave this as an exercise to the reader.

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