By: Kristen Shelton

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The Moebius Strip

• By Kristen Shelton
• MGF-1107
• November 21, 2000

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Do you see what I see?

• (This presentation is about seeing things
  one-sided. If you see things from only one point
  of view then you need to see this.)
• Q What is a moebius strip and where did it
  originate?
• A A moebius strip is a one-sided figure formed
  by a two-sided strip. Is known for its
  characteristic of a one-sided continuous side.
• It originated from a the discovery made by a
  man by the name of August Ferdinand Moebius.

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August Ferdinand Moebius

• Moebius was a famous German Mathematician who is
  has been of great importance in the field
• of topology. He was
  a descen-
• dant of Martin
  Luther.He was
• educated at home
  and later
• attended school at The
  College in Schulpforta. He also became a student
  at the University of Leipzig.

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A. F. Moebius cont.

• He is responsible for the discovery of a
  one-sided but two dimensional surface. We call it
  the Moebius Strip.
• ---INSERT PICTURES HERE---
• For more interesting facts about A.F. Moebius
  click here.

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Make Your Own

• Its easy, just
• 1.) Cut a strip off a piece of notebook paper.
  (cut off of the long side).
• 2.) Give one end of the strip a twist.
• 3.) Connect the ends together and tape.
• If you did it right is should look like
  this
• Follow the edge of the paper
• and See if you can continue
• to follow It around and round.
• If you can its a true
• Moebius Strip!
• http//www.pbs.org/wgbh/phenom/mobiusstrip.html

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Where can you find a Moebius
Strip?

• Recording tapes
• Sports
• Industry
• Art work
• A. F. Moebius created a new idea
• and dimension that is commonly used today.
• Lets see some of these examples.

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Moebius Strips in the Making

• Moebius strips were used in designing cassette
  and video tapes. If you look inside at the film,
  you will notice that the way the inside is
  wrapped around it resembles the moebius strip you
  just made.
• This idea gave tapes double the
• recording time. Isnt that nice?!

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Moebius in Motion

• (For all you sports fans)
• Many famous free style skiers have a stunt
  
• where they perform a jump and a twist which
  they call the
• Moebius Flip. Interesting enough, they
  arent really
• making a Moebius
  band.

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Moebius Making Machines

• In Industry, the Moebius Strip was applied
  to the making of large conveyor belts. It made
  the work of the conveyor belts much more
  efficient in the same way it did the recording
  tapes. It wore the belts equally all the way
  around and allowed them to be used longer. Made
  for larger profit as well!

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The Art of the Moebius Strip

• (We all have an artistic side to us!)
• There is a famous artist by the name M.C. Escher
  that has a well-known piece of work because it
  portrays the one-sidedness of the Moebius Strip.
  He uses the characteristics of insects and their
  ability of finding their way up and free of a
  visible surface but if you place some insects
  on a Moebius Strip they would most likely follow
  each other around and round and so on.

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Moebius or Not?

• Which work of art is a Moebius band and
  
• which isnt?
• Why or why not?
• For more interesting art work by M.C. Escher
  just visit
• Http//users.erols.com/ziring/escher.htm
  works

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Making Things Stretch

• Here is what a Moebius Band/Strip would look
• like if we added a little color and curved all
  its
• edges into a circle.

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Conclusion

• Isnt neat how one little discovery could turn
  the world of Geometry upside down!
• Now when ever you see a Moebius band in one
  shape, form, or fashion, remember that its
  always best to look at life from another
  
  
• perspective.

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SOURCES

• www.scidiv.bcc.ctc.edu/Math/Mobius.html
• www.cut-the-knot.com/do_you_know/moebius.html
• www.groups.dcs.st-and.ac.uk/history/Mathematician
  s/Mobius.html
• www.rose.hulman.edu/berglunb/Mobius.html
• www.pbs.org/wbh/zoom/phenom/mobiusstrip.html
• http//users.erols.com/ziring/escher.htmworks