Comments on: How Many M&M’s Can Fit Inside a Klein Bottle?

By: nex

nex — Wed, 28 Feb 2007 10:04:43 +0000

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.

By: Denita TwoDragons

Denita TwoDragons — Sun, 28 Jan 2007 22:47:24 +0000

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

By: beajerry

beajerry — Sun, 28 Jan 2007 10:45:31 +0000

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.

By: Ty

Ty — Sun, 28 Jan 2007 04:39:10 +0000

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

By: MrPumpernickel

MrPumpernickel — Sat, 27 Jan 2007 13:13:54 +0000

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.

By: beajerry

beajerry — Sat, 27 Jan 2007 09:31:10 +0000

Not a true Klein bottle.