A few people have asked me about the geometry of the Klein bottle since I posted last time. I cant really go into too much more detail without you actually being here with me and giving 3d representations of it. Here is a video that should help to show the creation of a Klein bottle from its 2D-Manifold though. Essentially the way a M-Strip is twisted and connected to itself once....a Klein bottle is twisted and connected to itself on every point of its 3D surface (hard to imagine...why? Because you can only bend and warp 3 Dimensional space inside of the 4th dimension...thus making what you see here only a theoretical representation of the Klein bottle rather than its actual form.)
Thursday, April 5, 2007
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