Flat torus

Discussion of shapes with curves and holes in various dimensions.

Flat torus

Postby Secret » Fri May 04, 2012 10:31 am

http://www.sci-news.com/othersciences/m ... 00279.html
http://www2.cnrs.fr/en/2027.htm

What is its native number of dimensions?
Is it related to a clifford torus?

EDIT: Nevermind
http://docmadhattan.fieldofscience.com/ ... space.html

Now they should start flattening the other 4D objects such as RP2 and klein bottle!

P.S. That thing looks REALLY convoluted
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Re: Flat torus

Postby quickfur » Tue May 15, 2012 7:36 pm

The ridge of the duocylinder (which is related to the clifford torus) is a uniformly-deformed torus. It's not quite flat, because there is still deformation, but it's different from a 3D torus where deformation is non-uniform. However, I don't think the duocylinder ridge is what they're talking about here. I'm not sure I understand how the smooth fractal makes it non-deformed. If anything, I'd say the duocylinder's ridge is closer to being a "faithful representation" of the flat torus. But I may be biased. ;)
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Re: Flat torus

Postby wendy » Wed May 16, 2012 7:33 am

It's little to do with four dimensions.

What the picture shows is a square folded into a torus in three dimensions. That is, it's more like a crumpled piece of paper. Cut it in the two directions, and uncrumple it, and you get a square.
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