Posted on 07/16/2007 6:50:45 AM PDT by SubGeniusX
Scientists say they have cracked a nearly eight-decade-old riddle involving the Moebius strip, a mathematical phenomenon that has also become an icon of art.
Popularised by the Dutch artist MC Escher, a Moebius strip entails taking a strip of paper or some other flexible material.
You take one end of the strip, twist it through 180 degrees, and then tape it to the other end.
This creates a loop that has an intriguing quality, dazzlingly exploited by Escher, in that it only has one side.
Since 1930, the Moebius strip has been a classic poser for experts in mechanics. The teaser is to resolve the strip algebraically - to explain its unusual shape in the form of an equation.
In a study published on Sunday that lyrically praises the strip for its "mathematical beauty," two experts in non-linear dynamics, Gert van der Heijden and Eugene Starostin of University College London, present the solution.
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.
If the width of the strip increases in proportion to its length, the zones of energy density also shift, which in term alters the shape, according to their equations.
A wider strip, for instance, leads to nearly flat, "triangular" regions in the strip, a phenomenon that also happens when paper is crumpled.
The research may seem esoteric, but Mr van der Heijden and Mr Starostin believe it also has practical applications.
It could help predict points of tearing in fabrics and also be useful for pharmaceutical engineers who model the structure of new drugs.
The Moebius strip was named after a German mathematician, August Ferdinand Moebius, who discovered it in 1858.
Another German, Johann Benedict Listing, separately discovered it in the same year.
This article seems awfully convinced that these guys have solved the puzzle. I don't know if that's true. If you ask me, this reporting is pretty one-sided.
The Moebius strip was named after a German mathematician, August Ferdinand Moebius, who discovered it in 1858.
Another German, Johann Benedict Listing, separately discovered it in the same year.
Ack. Nicely done. :-)
...nice..
Joseph Paper invented paper in 1857 so it only took a year.
Interesting. One sure can learn a lot on the internet!
If you strip away the thin layer of rhetoric, all that you’re left with is twisted logic...
ping
Here is what a learned mathematician has to say about the study...
"That is simply a mathematical parameterisation of the surface within 3 dimensional space. What the work in the article is talking about is describing the mechanical stresses a physical object with the shape of a Mobius strip will have upon it due to it's material strength and rigidity. As the article says, it's an important thing to understand if you're building fabric or chemical structures which twist in such a way."
They probably did, but there’s a difference between some guy gluing a piece of paper into a weird shape, saying “that’s cool” then throwing it away, and some science type doing it and writing a paper about it. In general stuff isn’t considered “discovered” until there’s published data about it.
ok... that was cool
I’m sure you’re right. When Mobius’s paper came out all across Europe there were guys digging through their trash out back thinking “Dang - I wish I hadn’t thrown that doodad out last month - it could have been the Vinkowyz strip instead of that darned Mobius strip.”
Could it be that your telephone cord crosses the Equator? ;’)
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