Results 1 to 4 of 4

Math Help - möbius strip

  1. #1
    Member
    Joined
    May 2008
    Posts
    75

    möbius strip

    Why is the möbius strip not orientable, in the sense that there cannot exist a globally defined continuous surface normal?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    This is demonstrated by triangulating the surface, and showing that the triangulation is not orientable.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2008
    Posts
    75
    Thanks for your answer! Unfortunately i do not know what a triangulation is. But this should work:

    Let us pick a continuous curve c on the strip. If we pick a normal vector at c(0) it will point in the other direction at c(2pi). This is geometrically obvious and we would have a contradiction. But how can i show that formally?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    The only formal proof that I know of uses the theory of simplical complexes!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Möbius transformation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 4th 2011, 11:59 AM
  2. Euler charateristics of the Möbius strip
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 10th 2011, 07:51 AM
  3. Sum of Möbius Function
    Posted in the Math Challenge Problems Forum
    Replies: 4
    Last Post: December 29th 2010, 12:37 PM
  4. conformal map, strip
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 7th 2010, 12:14 PM
  5. strip bonds
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 9th 2007, 07:19 AM

Search Tags


/mathhelpforum @mathhelpforum