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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

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Oliver Thewalthttp://rouxph.blogspot.fr/2013/01/du-ruban-de-mobius-la-bouteille-de-klein.html