Oliver Thewalt

    Oliver Thewalt

    Theoretical Physics | Quantum Biology | Dark Matter Research Cluster

    From Moebius Strip to the Klein's bottle by Phillipe Roux

    From Moebius Strip to the Klein's bottle by Phillipe Roux
    By Oliver Thewalt Comments (1)

    0/5 stars (0 votes)

    by Phillipe Roux, Google Plus

        From the Moebius strip to the Klein's bottle
    #KleinBottle is an amazing compact and closed #surface which cannot be embedded in R^3 without making self-intersections. To see this fact you can try to construct it starting from the #MoebiusStrip and trying to glue its opposite edges to close this surface ... of course this cannot be fulfilled in 3 dimensions without tearing up the Moebius strip!

    The animation presented here was build with #scilab , which fits perfectly to show 2D surfaces en 3 dimensions  using mesh and colors. It tries to  visualize how Klein's bottle is obtained from Moebius strip and how self-intersections arise. A slower animation is available in my previous post
    https://plus.google.com/118331054304456615935/posts/Z6p6pfSPPU6




     Another amazing fact about the Klein's bottle  : at first the object was named  "Kleinsche Fläche" ( that means « Klein surface » ) by German mathematicians  but soon after there was a mistake in translations  between Germans words  Fläche (« surface ») and  Flasche (« bottle ») which leaded to the actual name « Klein bottle » ... even in German !
     
     see also :
    http://en.wikipedia.org/wiki/M%C3%B6bius_strip
    http://en.wikipedia.org/wiki/Klein_bottle