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CTK Exchange
David Bump
guest
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Nov-01-08, 11:19 PM (EST) |
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"Moebius-cut torus"
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I "discovered" something I assumed had already been known, but I've searched in vain for a site that stated it plainly and clearly. It's this: If you cut a solid toroidal body while making a half-twist (following the path of an imaginary mobius strip embedded in the torus), the object remains in one piece, just as when cutting a mobius strip along its centerline. A true torus would also remain in one piece, but I think it is more dramatic with a common, solid body such as a donut. |
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alexb
Charter Member
2299 posts |
Nov-09-08, 08:37 AM (EST) |
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1. "RE: Moebius-cut torus"
In response to message #0
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>... I think it is more dramatic with a common, solid
>body such as a donut. Yes, I agree. I do not remember seeing this mentioned. One can start with flattening the torus, i.e. squeezing it (or by chiseling away) to make a flat surface. This can be done in many ways; and getting a Moebius strip is one possibility. This done, you can cut the Moebius strip along the midline and then think of what this corresponds to on the original torus. The trace of your "knife" actually gives one possible flattening. The normal to that Moebius strip is the second "knife" that produces the same result. Very nice. Thank you.
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