Loopy logic: A Möbius strip made of a material that changes colour with bending pressure. 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.
Credit: Nature Materials/Starostin & van der Heijden
PARIS: Scientists have cracked a 75-year-old riddle involving the Möbius strip, a mathematical phenomenon that has also become an art icon.
Popularised by the Dutch artist M.C. Escher, a Möbius (or 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.
See Escher's Möbius Strip II (1963) from the M.C. Escher Foundation web site.
Mathematical conundrum
Since 1930, the Möbius 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.
Now, in a study published in the journal Nature Materials that lyrically praises the strip for its "mathematical beauty," Gert van der Heijden and Eugene Starostin of University College London, in England, present the solution.
What determines the strip's shape is its differing areas of "energy density," say the experts in non-linear dynamics.
"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.
Not just esoteric
The research may seem esoteric, but van der Heijden and 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.
"One of the classic problems in mechanics is to find the shape assumed by a Möbius strip – the famous band that is closed with a half-twist and which has the intriguing topological property that it only has one side," said mathematician John H. Maddocks in an accompanying commentary that also appeared in Nature Materials.
"This abstract mathematical question, dating back to at least 1930, is also of practical scientific interest as single crystals in the form of a Möbius band have now been grown," said Maddocks, of the Swiss Federal Institute of Technology in Lausanne, who was not involved in the study.
The Möbius strip was named after a German mathematician, August Ferdinand Möbius, who discovered it in 1858. Another German, Johann Benedict Listing, separately discovered it in the same year.
Moebius Strip Sci-Fi novel.
I just recently read D. Richard Lewis' sci-fi novel called: "TIME TRIP ON A MOEBIUS STRIP," and it ties in, or should I say, "twists in," pretty well with this new theory these two scientists came up with explaining the riddle of the Moebius strip... The plot in this sci-fi novel is quite interesting...The author has this marine biologist discover a giant nautilus shell on the beach and then with the help of the great grandson of Professor Moebius, constructs a giant metal Moebius strip in the shell...The marine biologist then rides a vehicle upon the strip and enters another dimension where he then meets 16 famous missing people of history who have arrived in this time-less domain via a cloud...There is an angel in the story as well... The author has also discovered many amazing connections that these lost famous people have with eachother...I was in awe by them...Carl Jung would have probably tried to tie these connections in with his theory of "archetypes," which is what the author does through one of the lead characters who is a woman psychiatrist. The novel was a great feat of historical research and quite original...A++++
Re: Sci-Fi Novel
Sorry, any validity flew out the window at the mention of "16 famous missing people of history arriving on a giant cloud -- also, there's an angel."
Obviously
Yes. SCI-FI NOVELS (!) just aren't worth reading unless they're jam packed with validity.
The Sci-Fi Novel: "TIME TRIP ON A MOEBIUS STRIP"
I am the author of the sci-fi novel: "TIME TRIP ON A MOEBIUS STRIP" and the 16 famous people in my story who disappeared mysteriously did not all arrive on a single cloud to the timeless dimension, but were each transported there..If you had read the novel you would have learned of the connections I discovered that 10 of the 16 people had with the goddess Aphrodite, the Virgin Mary, and roses, which connect them both. I also talk about the many theories concerning the Moebius strip.
Some of the people in my novel are: George Leigh Mallory, Jimmy Hoffa, Glenn Miller, Martin Bormann, Antoine de Saint Exupery, Joe Kennedy Jr, Anastasia Romanov, Raoul Wallenberg, Tsar Alexander the First, Judge Crater, Leslie Howard, D.B. Cooper, Roald Amundsen, Amelia Earhart, Michael Rockefeller, etc....Read the novel before judging it..For a sample page go to my blog at: http://moebiustripper.blogspot.com
LOL
And how you validate SCIENCE FICTION dumbass?
Author's reply to "LOL"
You ask: "How do you validate science fiction?" You wait until fiction becomes fact...And who says you have to validate it anyway? You are reading fiction...Can you validate God's existence? Can you validate President Obama's birth certificate? Because if you can, I've got some swamp land for sale in the Everglades I can show you...Now how's that for validation?
Does it not also have only
Does it not also have only one edge?
Yes.
Yes, it does. But this isn't exactly relevant. The "big thing" about it is that it only has a single side. A circle also has only a single edge, but this is the only shape to possess only a single side.
WRONG
A mobious strip has two sides. The surface of the strip, and the edge of the strip. Also, a circle has more than one side. A circle has THOUSANDS of sides, their just tiny enough to look like a curve. To make a truly 1-sided object, you must take the mobious strip a little further. Take a rectangular prism, twist it 90 degrees, and join the two ends to make a circle. This is a one-sided object. I have no Idea what this is called, but I call it the Mobius Prism.
What are you talking about?
If you take a rectangle & twist it 90 degrees that is not the same. All your doing is adjusting the formula to suit your argument. The mobious strip is only effective with a circle that demonstrates the continuity of time compared with just a plain circle. That would be the reason why the mobious strip resembles the symbol of infinity.