Dr Eugene Starostin and Dr Gert van der Heijden recently published the solution to a 75-year-old mystery.
The two academics have discovered how to predict the shape of a Möbius strip, the ‘endless ribbon’ which is obtained by taking a rectangular strip of paper, twisting one end through 180 degrees, and then joining the ends.
Dr Starostin and Dr van der Heijden realised that the shape can be described by a set of 20-year-old equations that have only been published online. Their letter to ‘Nature Materials’ demonstrates that these differential equations govern the shapes of elastic strips when they are at rest, and enable researchers to calculate their geometry.
“This is the first non-trivial application of this mathematical theory,” said Dr Starostin. “It could prove to be useful to other research communities, such as mechanics and physics.”
At the moment, their notes in Nature Materials are pay-per-view.
Eideard’s toes are twitching, HHopper’s hair is hurting, and my hair is on fire! It’s a shame there were no real links in the article, and google reveals nothing. I’ve stumped many kids (and adults) with a Möbius strip and a Sharpie, there’s nothing like a one-sided surface….
OK, let’s see them do the same with a Klein bottle:
http://www.kleinbottle.com/
Bubba – – that klein bottle just looks like a closed container? Whats the deal? I bought a pitcher in Peru. Pour water in, it doesn’t come out the spout you used–have to use a different one. Cant figure out how that works either. ((Fun stuff!))
I gotta know—what happens to life on earth when the poles reverse? Will we hoomans survive the radiation does? How long before magnetic protection is reestablished? I’ve google this a few times and these issues aren’t discussed.
Thanks.
A mathematician confided
That a Möbius band is one-sided,
And you’ll get quite a laugh,
If you cut one in half,
For it stays in one piece when divided
#1 – BubbaRay,
Don’t forget to cut the mobius band along the line you’ve drawn to show that it indeed does stay in one piece when divided.
So, did any of you get the comment the other day when I tossed a shout out to the Klein bottle regarding infinity and eternity?
#2, bobbo, Here’s a very good explanation of a one sided surface, the Klein bottle, with some nice illustrations:
http://plus.maths.org/issue26/features/mathart/index-gifd.html
As for magnetic pole reversal, at minimum Earth magnetic flux, there will be some deleterious effects for organic life, but none life threatening for humans:
http://www.pbs.org/wgbh/nova/magnetic/
Hope that helps.
#4, BobH, I must have missed. Sorry.
#3, Scott, Isn’t that amazing? I’ve performed that “trick” for kids and adults — it’s fun to watch their faces light up.
Topology — it’s not just for fun anymore. Nanotubes, buckyballs, the list goes on. Darnit, the scope of this topic is way outside the bounds (or interest) for this blog.
5–Two excellent websites. Thanks. I’ll cancel that order for the lead panama hat asap!
Years ago I experimented with Mobius strips. I made a really wide strip so that I could cut it all the way around the center more than once. Try it sometime. The results are quite amazing. The more times you cut it, the crazier it gets.
I don’t know, judging by the graphic, the concept looks like it still has a few bugs to me.
BubbaRay…
http://www.dvorak.org/blog/?p=12799#comments
“Take the concept of infinity. If it helps, by all means add the twist of greater or lesser infinity numbers or map space onto a Kline bottle… whatever gets you sufficiently bent about synaptically speaking.
OK, big deep breath, now, with I N F I N I T Y staring back from the void, slide the word ‘eternity’ into ye olde cerebellum. Yes, that’s it… juxtapose those two back and forth. Infinity – Eternity & Space – Time.”
#10, BobH, I did comment about that — now it’s “Man, Woman, Birth, Death, Infinity.” Who said that??
http://www.dvorak.org/blog/?p=12799#comment-721021
But should you desire further exploration, you could try here, this gives me apeirophobia.
http://www.pbs.org/wgbh/nova/archimedes/contemplating.html
BubbaRay…
“Ben Casey was a drama series which ran on ABC from 1961 to 1966. The show was known for its iconic opening titles, which consisted of a hand drawing the symbols “♂, ♀, *, †, ∞” on a chalkboard, as cast member Sam Jaffe intoned, “Man, woman, birth, death, infinity.”
–source Wikipedia
The trip is when one juxtaposes Infinity and Eternity in the mind. Space/time gets to you rather quickly if you can but envision the universe as multiple infinite space(s) and thus eternity becomes multiple eternal time frames.
#12, BobH, …the symbols “♂, ♀, *, †, ∞” on a chalkboard, as cast member Sam Jaffe intoned, “Man, woman, birth, death, infinity.”
I doubt I ever missed a single episode of “Ben Casey”, for the time period it was one heck of a show.
I hope you enjoyed the link in post #11. String theory and multiple dimensions too small to detect are almost beyond comprehension — the math seems to work, some of the infinities cancel, but the physical embodiment of the results makes my cat walk right through walls.
Unfortunately, most string theory makes no testable predictions. Jury’s still out.
A brilliant man had this to say about my infinite wisdom:
“Only two things are infinite, the universe and human stupidity and I’m not sure about the former” — Albert Einstein
Recording tapes and conveyor belts are manufactured in the form of a Mobius strip? How does that work?
#14, Mr. Mustard, by golly there are cassette tapes with a half twist. But since the tape starts out as two-sided, both sides must be coated with ferromagnetic material. Cheese, you learn something new every day!
http://www.freepatentsonline.com/4924338.html
And conveyor belts too!
http://www.math.unh.edu/cgi-bin/generatePage.cgi?moebius
Huh. You DO learn something new every day, Mr. Ray!
And perhaps I’m just wooden-headed, but I’m still not sure I get the utility. For example:
>>This belt has two and a half twists and has an advantage
>>over conventional belt systems in that only the clean side
>>of the belt is in contact with the idlers on the underside.
OK. But what advantage does it have over a non-Mobius belt with NO half twists, where it would appear that only the clean side of the belt would also be in contact with the underside idlers?
#16, Mr. Mustard, “B. F. Goodrich Company patented a conveyor belt that it went on to produce as the Turnover Conveyor Belt System. Incorporating a half-twist, it had the advantage over conventional belts of a longer life because it could expose all of its surface area to wear and tear.”
Two and one half twists might have been used for tensioning or cleaning purposes, but that is pure conjecture on my part.
Mr Ray, I’m afraid I’m just too dense to get this. I see that exposing all surfaces would reduce wear and tear, but that would put the kibosh on the “one side only” against the idlers benefit. Two half twists would bring back the “one side only” benefit, but would get rid of the wear and tear reduction
There is a great sci-fi novel about the Moebius Strip…It is called: “TIME TRIP ON A MOEBIUS STRIP.” The novel is about 16 missing famous people of history who find themselves transported, via a cloud, to a timeless dimension…The main character is a marine biologist who enters this other dimension by riding a giant metal Moebius strip he constructs with the help of the great grand-son of Dr. Moebius…They place the Moebius strip inside of a giant nautilus shell that the marine biologist finds on the beach when he was a boy…There is also an angel in the story that 14 of the missing people have had contact with before becoming lost…I loved this book…A++++