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Möbius Strip Riddle Solved
BigLug writes with news that two experts in non-linear dynamics, Gert van der Heijden and Eugene Starostin of University College London, have developed an algebraic equation that describes the Möbius strip — something that, you may be surprised to learn, had never been done since the form's discovery in 1858. ABC.net.au has an accessible short summary: "What determines the strip's shape is its differing areas of 'energy density,' they say. 'Energy density' means the stored, elastic energy that is contained in the strip as a result of the folding. Places where the strip is most bent have the highest energy density; conversely, places that are flat and unstressed by a fold have the least energy density."
First I got slightly excited, then I realized that people are talking about Moebius strip as a physical object rather than mathematical.
And I lost interest. Does it qualify for "inaccurate"? I do not know.
I do not believe in karma. "Funny"=-6. Do good and forbid evil. Yours, Oft-Offtopic Flamebaiting Troll.
The discoverers got an article written about their paper, and it was linked to by Slashdot.
(Was that too subtle? I half expect "Offtopic" and "Troll" mods instead of the "Funny" I was going for.)
The paper in question, however, was modeling the minimum-energy state that a Möbius strip would adopt assuming that the local energy on the strip is based on local curvature (and that stretching energies can be neglected). As they point out, this is a very good approximation for building a Möbius strip by bending common thin materials (e.g. a sheet of paper or plastic). Knowing stress distributions is of course important for things like failure mechanics.
They also note that in the field of synthesizing nano-ribbons and nano-Möbius strips (yes, it's been done!), this bending energy can be critical to understanding the behavior of the final object, and is also important in understanding how such objects can be synthesized. (The growth of anisotropic nano-crystals, including nano-ribbons, is strongly dependent on the relative energies of the various growing surfaces.)
Having said all that, I think it's pretty clear that the authors tackled this particular mathematical problem because it was fun, and because of the notoriety of the Möbius strip. Ultimately it's a neat piece of mathematics and makes for some cool-looking graphs.
I know this is just flamebait, but you are aware that all of the modern disease cures are built on heavy amounts of basic math developed by previous generations of mathematicians, right?
"Who is the Journal of Quantum Physics going to believe?" --Stephen Hawking
In a similar way, if you used this formula to generate a mobius strip in the 3D program of your choice and then print it out on a 3D printer, it ceases to be a true mobius strip and becomes an object that is shaped like a mobius strip. it is a subtle, but definable, difference.
Wouldn't that apply to anything made of atoms regardless of whether it's produced on a 3D printer, carved from stone, or whatever? I'm thinking of the atoms as similar to 3D pixels - even a mobius strip assembled atom by atom is bumpy at the atomic scale and not representative of the pure mathematical form.
Putting moderation advice in your
Ben Hocking
Need a professional organizer?
..a stupid article. No just playing. I'm confused because the article didn't seem to present a case for what problems existed and exactly what they did to solve those problems. Oh a couple side notes for the publisher. First please let us know when the full details of the article require a paid subscription. Second, please make links with a target of _blank so that we don't get taken away from our beloved /.
I don't have an answer to your question, but your assumption certainly begs the question: Are you sure about that?
Begging the question does not mean raising the question.
Give me Classic Slashdot or give me death!
This will give me a Möbius strip with uniform stresses throughout
Uh, no. Even if you just take your perfect piece of paper and twist it slightly, you'll get a non-uniform stress distribution.
Think about it this way. Take your hands and put them together firmly. Slightly twist your left hand, trying to move your left thumb upwards and away from you. What's the sheer stress on your right hand due to the torque? It's upward near your palm, and downward towards your finger tips. That means its zero somewhere in the middle. This is a non-uniform stress distribution. The same thing will be true for adjacent slices of the flat sheet, even a mathematically perfect one.
A deep unwavering belief is a sure sign you're missing something...
But if most everyone thinks it does, it might as well.
When I hear someone trot out the "modern, popular usage" of "beg the question" or, say, "enormity" or "irregardless," well, I know those things are sanctioned by more populist dictionaries, but I pretty much assume the person is just using words they don't understand, which gives me a negative impression of them. And when people defend those usages, I think "here is someone who can't stand to find out they were wrong about something."
I'm awake! The answer is BONK!
I know this is just flamebait, but you are aware that all of the modern disease cures are built on heavy amounts of basic math developed by previous generations of mathematicians, right?
And sadly, the work of many generations of mathematicians is utilized by idiots so that they can drive their SUV, eat a fast-food hamburger, and talk on the cell phone all at the same time.
(As for me, I'm an EE. Sometimes I think about others I knew who were working several years toward their PhD. It's actually quite (morbidly) funny...)
Personally, I have renewed respect for janitors and garbage collectors. Without R&D folks, *technology* would no longer advance. Without janitors/garbage people, *populations* would cease to exist.