MadSci Network: Physics
Query:

Re: Are there any mobius strips occurring in nature?

Date: Mon Feb 21 14:20:01 2000
Posted By: Adrian Popa, Directors Office, Hughes Research Laboratories
Area of science: Physics
ID: 944628842.Ph
Message:


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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