History of the Mobius

Week 18 = Mobius from Cast On to Bind Off

Day 3 = May 2, 2014

     The knitted Mobius is modeled after a mathematical object, the Mobius Strip. Who would have thought there was so much math in Knitting? ;-) Just for fun, here is Wikipedia's entry on Mathematics and Fiber Arts. It is very interesting.
    
     Here are several excerpts and photos from the Wikipedia entry on Mobius Strip:

  August Ferdinand Mobius

     "The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmoʊbiəs/; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.^[1][2][3]"

     "The Möbius strip has several curious properties. A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip. This single continuous curve demonstrates that the Möbius strip has only one boundary."

     "A scarf designed as a Möbius strip."

      "A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having traversed the entire length of the strip (on both sides of the original paper) without ever crossing an edge."

How to create your own paper Mobius:

1. Take an 8-1/2" by 11" piece of paper.
2. Tear off a strip length wise about 1" wide so you will have a 1" by 11" strip.
3. Draw a dotted line down the middle of one side.
4. Hold the strip out and turn one end over so that there is a twist in the paper.
5. Now join the ends with a piece of tape.

     There you have a Mobius! If you follow the line you drew, it does not go all the way around. Continue to draw your line and it will meet back at the beginning of your original line. So, because of 1 simple half-twist, you have an infinite path and an unending edge.

     In simpler terms, the Mobius is like a 3 dimensional figure 8. Maybe that is why I am so fascinated with the Mobius! When I was in school I loved drawing and doodling figure 8's over and over again because they never ended and were much "fancier" that a plain old 0.

     I will have an update for you on my Cuddle Shrug Mobius tomorrow. Plus,
don't forget about our MAY Giveaway. To see the rules of the giveaway, click here.

Knitting question of the day

Have you ever knitted any Mathematical things like this before? If so what?

Knitting,

Victoria

References

1. Jump up ^ Clifford A. Pickover (March 2005). The Möbius Strip: Dr. August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology. Thunder's Mouth Press. ISBN 1-56025-826-8.
2. Jump up ^ Rainer Herges (2005). Möbius, Escher, Bach – Das unendliche Band in Kunst und Wissenschaft . In: Naturwissenschaftliche Rundschau 6/58/2005. pp. 301–310. ISSN 0028-1050. 
3. Jump up ^ Chris Rodley (ed.) (1997). Lynch on Lynch. London, Boston. p. 231.