Tue 19 Feb 2008
I learned something new today from Myles. I always seem to be learning new things from him. What I’d really like to learn is to cook as well as he does. *grin*
I was never good at spatial reasoning unfortunately. Didn’t fare well in that portion of standardized tests sadly. This information is gacked from wikipedia. But of course
A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a single strip. In Euclidean space there are in fact two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. The Möbius strip is therefore chiral, which is to say that it is “handed”.
It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.
Art and Popular Culture
The Möbius strip has provided inspiration both for sculptures and for graphical art. The artist M. C. Escher was especially fond of it and based several of his lithographs on it. One famous example, Möbius Strip II, features ants crawling around the surface of a Möbius strip. It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke’s The Wall of Darkness. Science fiction stories sometimes suggest that our universe might be some kind of generalized Möbius strip. This is especially prominent in the Perry Rhodan-series. In the short story “A Subway Named Moebius”, by A.J. Deutsch, the Boston subway authority builds a new line, but the system becomes so tangled that it turns into a Möbius strip, and trains start to disappear. The Möbius strip also features prominently in Brian Lumley’s Necroscope series of novels.
The mobius strip is even the signature architectural feature of the NASCAR Hall of Fame (www.nascarhalloffame.com), presently under construction in Charlotte, NC.