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Mobius Strip as Source of Infinity Symbol?

Date: 03/31/2005 at 04:09:09
From: Colin
Subject: Infinity Symbol

There are questions on this web in regard to the infinity symbol,
which is actually a representation of a Mobius strip--a strip twisted
once and joined at the ends.  It is not in fact a lazy eight although
written as such.  The widening of the figure (twist in the Mobius
strip) is usually over the center of it and in front extending back to
thin lines at left top and right bottom.

I thought I ought to point this out as no one else has.



Date: 03/31/2005 at 10:08:39
From: Doctor Peterson
Subject: Re: Infinity Symbol

Hi, Colin.

There is little chance that the symbol originated as a Mobius strip, 
since the latter was invented in the 1800's, and the symbol is 
hundreds (in a sense thousands) of years older.  It's a common 
misconception, though.

If this is the page you read, then you can see that the symbol was 
used for infinity 200 years before Mobius:

  Origin of the Infinity Symbol
    http://mathforum.org/library/drmath/view/57551.html 

But it was in use for other purposes long before that, as you can see 
near the middle of this page, which discusses in detail the origin of
the symbol:

  Earliest Uses of Symbols of Calculus
    http://jeff560.tripod.com/calculus.html 

  Cajori (vol. 2, p 44) says the conjecture has been made that
  Wallis adopted this symbol from the late Roman symbol oo for
  1,000. He attributes the conjecture to Wilhelm Wattenbach (1819-
  1897), Anleitung zur lateinischen Paläographie 2. Aufl., Leipzig:
  S. Hirzel, 1872. Appendix: p. 41. 

Your story is referred to as "possibly apocryphal" here:

  Mobius Strip
    http://en.wikipedia.org/wiki/Mobius_strip 

  The Möbius strip is often cited as the inspiration for the
  infinity symbol, since if one were to stand on the surface of
  a Möbius strip, one could walk along it forever. However, this may
  be apocryphal since the symbol had been in use to represent
  infinity even before the Möbius strip was discovered.

Note that the Mobius strip is no more "infinite" than a circle, which 
has more ancient associations with infinity than the strip.  I've 
never seen any documentation to back up the theory, or even evidence 
that the Mobius strip was known two hundred years earlier, and without 
that, I wouldn't be as generous as the author of the article above!

Of course the symbol didn't originate as a "lazy eight", either; I  
don't know of anyone who says it did.  That term is a description 
(often used with kids), not a historical statement.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 03/31/2005 at 16:52:58
From: Colin
Subject: Thank you (Infinity Symbol)

Thank you very much for your pleasant reply, and I agree that it is a
problem for those folks who purport the Mobius as the Infinity symbol
to prove its existence at an earlier date.  As far as I know it was
used in some occult practices so there is little chance of it being
proven.
 
Have a good day!

- Col
Associated Topics:
High School History/Biography

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