The Möbius Strip Unraveled
Ever wondered why it is that your telephone cord will coil both to the left and to the right? Well children the world over have seen the answer to this riddle, according to researchers Eugene Starostin and Gert van der Heijden, both of University College London. They’ll discover it in the science rooms of their schools, or in their own time, and all they need is one single strip of rectangular paper.
It’s the Möbius Strip, and it has baffled mathematicians for more than 75 years and stupefied artists for even longer. Möbius Is a 3 dimensional representation of the infinity symbol (∞) and can be created by simply taking a piece of rectangular paper, twisting it, and tacking the ends together"…whatever path you take, you always end up where you started,” describes Starostin.
A Möbius Strip is defined as a Developable surface, or, a surface which when flattened retains its shape. When a developable surface is formed in to a Möbius Strip, it will naturally try and change back to Möbius Strip a state of minimum stored elastic energy. It is this form that has eluded mathematicians for nearly 75 years, since the first papers looking at this problem were first published.
The theory is based upon a set of unpublished equations from 20 years ago. "This is the first application of this mathematical theory. Other communities, such as experts in mechanics, don't know of its existence,” says Starostin. "The equations apply to any rectangular strip that twists and bends. They might be useful for carbon nanotubes, for example, which are made of sheets of carbon."
It is an understanding of this quandary that could result in the less fulfilling answer, why do telephone cords coil both ways?
If you’re wondering where you might have seen a Möbius Strip, then here are a few applications; they are used for conveyor belts so that every surface acquires equal attention, and it allows for cassette tapes to record for double the time. In pop-culture and art, many appearances of the design are found, with artists such as M.C. Escher showing a great deal of interest in the shape. Make sure to check out one of his most famous lithographs here, depicting ants traveling across a Möbius Strip.
There is a way to fold a Mobius strip flat. I discovered it in 1968, when I was trying to figure out how to include my cyclical poem, "Doing the Mobius Strip," which is written on a Mobius strip, in a manuscript. I solved the problem by devising a way to fold the poem-containing strip flat and putting it in an envelope, which I included as a page in the manuscript.
If you're interested in the method, leave a comment here.
Posted by: Jack Butler | July 17, 2007 at 09:48 AM