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

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
Posts: 159
Joined: Tue Jul 06, 2010 12:03 pm

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. ;)
Posts: 2298
Joined: Thu Sep 02, 2004 11:20 pm
Location: The Great White North

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.
The dream you dream alone is only a dream
the dream we dream together is reality.
User avatar
Posts: 1650
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Return to Toratopes

Who is online

Users browsing this forum: No registered users and 1 guest