| MadSci Network: Physics |
Greetings:
The answer to your question is YES. Nature can have Mobius like structures.
Your question is an interesting one for I first read about the odd
attributes of Mobius strips when I was in highschool way back in the 1940s
in a now famous paperback book by George Gamow titled "One, Two, Three
Infinity". Most of the scientists of my era recall reading that particular
book at an early age. I made a quick straw poll of several scientists near
my office and none of them knew of any natural form of the Mobius strip.
However; I continued to search the web and hundreds of oddball sites came
up. It seems that dozens of people use Mobius strips to questionably (at
least to me) describe complex issues beyond the scope of science and
mathematics.
I searched the patent database and found 16 patents with Mobius in the title
including toy puzzles, band saw blades, long lasting typewriter ribbons and
even an interesting particle accelerating grid. For your information these
patents are listed below.
US05678489 10/21/1997
Electrically-operated moving body travelling on a rail capable of explaining
free quadrants described in the mobius theorem
US05557178 09/17/1996
Circular particle accelerator with mobius twist
US05324037 06/28/1994
Mobius strip puzzle
US04968161 11/06/1990
Ribbon cassette for reinking only one longitudinal half of a Mobius ribbon
US04640029 02/03/1987
Mobius strip and display utilizing the same
US04599586 07/08/1986
Mobius capacitor
US04384717 05/24/1983
Mobius strip puzzle
US04253836 03/03/1981
Mobius belt and method of making the same
US04189968 02/26/1980
Mobius strip bandsaw blade
US04058022 11/15/1977
Mobius drive belt fastener
US04042244 08/16/1977
Mobius toy
US03991631 11/16/1976
Woven endless belt of a spliceless and Mobius strip construction
US03953679 04/27/1976
Telephone answering device utilizing Mobius loop activating switch
US03758981 09/18/1973
MOBIUS BAND TYPE AMUSEMENT DEVICE
US03648407 03/14/1972
DYNAMIC MOBIUS BAND
US03621968 11/23/1971
RIBBON CARTRIDGE WITH MOBIUS LOOP IN RIBBON
Finally talked with a chemist and he said check on chiral molecules and sure
enough I found pay dirt at the following web site:
http://
www.rod.beavon.clara.net/chiralit.htm
QUOTE: "A chiral molecule is one that is not superimposable on its mirror
image. Non-superimposability on the mirror image is a necessary and
sufficient condition for chirality; no exception has ever been found. The
non-superimposability can come about in a number of ways, and need not
involve a chiral
center, or even organic molecules at all. Some examples are amusing; since
amusement is by far the best reason
to do any Chemistry, here are some examples, after a brief excursion into
the topic of optical activity. The
examples are from March (1).
Optical activity:
The degree of rotation of the plane of polarization of plane-polarized
monochromatic light by a chiral compound
depends on the path length the light traverses, the concentration of the
compound (if it is in solution), the
compound itself – and the wavelength of the light. It is not widely
promulgated that the amount of rotation a
particular sample gives is wavelength dependent, a phenomenon called optical
rotatory dispersion. The light
usually used for the determination of optical activity is sodium light; at
other wavelengths, the rotation will be
different, may be zero, and may even reverse in direction compared with the
rotation given with sodium light.
------------------------
Perchlorotriphenylamine (the 'perchloro' bit derives from the replacement
of all of the hydrogen atoms with chlorine) is heavily sterically hindered
and the molecule is in the shape of a propeller.
Perchlorotriphenylamine
Perhaps you have at some time cut a strip of paper, glued one end, and then
joined the two ends with a half-twist: the Mobius Strip. You can then
convince yourself using a pencil that this strip has only one surface. I
think it's highly amusing that chemists have done the same thing with a
molecule (2). Note that the bonds are not O-O
bonds, but each has a -CH2CH2- group between them. These are omitted for
clarity.
END QUOTE
The following is my rough drawing of the double ringed
perchlorotriphenylamine molecule With the two rings attached by carbon
bonds. The Mobius twist between the rings is located at the X in the
drawing. The rings are actually one above the other except at the twist, I
flattened the rings out to simplify my drawing. The web site has a much
better 3D picture.
C – O O – 0 – C
/ \\ X //\
O C – O O – O – C O
\ \ / /
\ O O /
\ \ / /
O O O O
\ \ / /
\ O O /
\ \ / /
O C O
\ II /
\ -C-/
Best regards, Your Mad Scientist
Adrian Popa
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