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Klein Pasta
Topological impossibilities (al dente) in a creamy tomato sauce. | |
Klein bottles, the bottles with no definite outside/inside surface are
extremely beautiful, but rarely seen out of a science museum. Making
them into pasta would not only make dinner look pretty, it could also
be used to teach basic topology to kids (there could be an explaination
on the packet).
Theyd be quite hard to make, so they would have to be
quite large... maybe 4 or 5 in your average bowlful, but they would be
interesting to dissect to see the inner workings.
'Acme' Klein bottles.
http://www.kleinbottle.com/
I really like the look of the Klein hats too... [up_on_cloud_nine, Dec 13 2008]
Moebius Pasta
Moebius Pasta
Not dissimilar [zen_tom, Dec 15 2008]
[link]
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[MaxwellBuchanan] could help. He's a freelance topologist. |
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By the way, I've bought some kleinbottles from Acme and they're great. And I'm nothing to do with them! |
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An opaque Klein bottle is hard to appreciate. I wonder, does translucent pasta exist? |
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glass noodles are translucent... they might not taste nice
with creamy tomato sauce, though - I'd have to change the
tagline.... |
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I never understood the fuss over Klein bottles. The certainly have a volume, that of the neck thats inside the bottle subtracted from the volume of the bottle. Warp it about a bit and you have a standard bottle. Whats the big deal? |
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//interesting to dissect to see the inner workings//
the *what* workings ? |
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The ones on the inside, I think. |
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//the *what* workings ?//
apologies.
The interesting pipework which may or may not be percieved as 'inner' |
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//He's a freelance topologist//
I've got a privet hedge that I want to look like steam locomotive -would he be able to help? |
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[Voice] What are sold as Klein bottles are only a three dimensional representation. Just like a mobius strip has only one two dimensional surface due to a twist in 3 dimensions, a klein bottle has a single enclosed volume that contains the entire universe due to a twist in 4 dimensions. It's not possible to construct one, just an approximation. |
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[MechE] is trying to see just how much rubbish he can get away with spouting until someone calls him on it! |
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//[MaxwellBuchanan] could help. He's a freelance topologist.
// Freelance *consultant* topologist. I can only advise, at
least until I get my licence back. |
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[Wags] You're right, that was rubbish. I misstated some of the basic topology. Where a mobius strip is a single surface with a single edge, a Klein bottle is a single surface with no edges. This can be done by taking 2 mobius strips and joining the edges of one to the edges of the other. Unfortunately, this is the step that can't be done in 3 dimensional space without the two strips intersecting themselves, which prevents it from being a single continous surface. |
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That being said, I have no problem with the idea of mathematically representive pasta, I just want Klein bottle pasta that has a little space tear in the middle of it.
(Better rubish this time?) |
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The hypothetical "real" klein bottle being discussed here would be awesome, but the kind that they actually make and sell and that this pasta would have to be I've always found really ridiculous. |
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It's not elegant at all. There's a huge and obvious edge around the hole right where the tube goes inside the bottle. Which also happens to be a perfectly reasonable and non-arbitrary point to label as where the outside of the bottle changes to the inside... |
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It would still taste nice. |
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I think they'd fill with water during boiling, and ve very hard to empty. It's hard enough to drain Conchilini. |
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But they have no volume... how do they fill with water? |
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// But they have no volume... how do they fill with water?// |
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Topologically, a klein bottle has one surface. But that doesn't mean it won't hold water. Topologically, a bowl only has one surface too. |
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So whats the mobius strip equivalent of a klein bottle being able to hold water or not? |
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//Topologically, a klein bottle has one surface. But that doesn't mean it won't hold water. Topologically, a bowl only has one surface too.// |
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That's a point.... still, if you used a colander you'd probably empty it. |
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