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Like the image above is very similar, just an edge-framework, so apparently the square are faces on the torus surface, and the 23,29-gonal polygons are ignored? Tom Ruen ( talk) 05:45, 7 February 2011 (UTC)
And is a Clifford torus the same as a duocylinder?? Tom Ruen ( talk) 05:51, 7 February 2011 (UTC)
The comment(s) below were originally left at Talk:Clifford torus/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I wrote this page a while back and nobody else has edited it since. More applications are needed and some history would be nice. VectorPosse 18:13, 11 May 2007 (UTC) |
Last edited at 18:13, 11 May 2007 (UTC). Substituted at 01:53, 5 May 2016 (UTC)
And why is it named Clifford? — Tamfang ( talk) 23:10, 4 February 2017 (UTC)
The description of the Clifford torus as an example of "Euclidean geometry" is surely wrong. The Euclidean plane is equivalent to , but the Clifford torus is equivalent only to a finite subset. If you set up a Cartesian coordinate system with the origin at the centre of the fundamental square, it will bump into itself across the joining zippers, where finite coordinate values must suddenly change sign. If you adjust the metric to be infinite at the zippers (known to some geometers as the absolute line) then Euclidean geometry will never reach them and the square is not even joined up to become a torus. Sure it is locally Euclidean, but then so is any smooth coordinate manifold. — Cheers, Steelpillow ( Talk) 11:57, 12 November 2019 (UTC)
This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Like the image above is very similar, just an edge-framework, so apparently the square are faces on the torus surface, and the 23,29-gonal polygons are ignored? Tom Ruen ( talk) 05:45, 7 February 2011 (UTC)
And is a Clifford torus the same as a duocylinder?? Tom Ruen ( talk) 05:51, 7 February 2011 (UTC)
The comment(s) below were originally left at Talk:Clifford torus/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I wrote this page a while back and nobody else has edited it since. More applications are needed and some history would be nice. VectorPosse 18:13, 11 May 2007 (UTC) |
Last edited at 18:13, 11 May 2007 (UTC). Substituted at 01:53, 5 May 2016 (UTC)
And why is it named Clifford? — Tamfang ( talk) 23:10, 4 February 2017 (UTC)
The description of the Clifford torus as an example of "Euclidean geometry" is surely wrong. The Euclidean plane is equivalent to , but the Clifford torus is equivalent only to a finite subset. If you set up a Cartesian coordinate system with the origin at the centre of the fundamental square, it will bump into itself across the joining zippers, where finite coordinate values must suddenly change sign. If you adjust the metric to be infinite at the zippers (known to some geometers as the absolute line) then Euclidean geometry will never reach them and the square is not even joined up to become a torus. Sure it is locally Euclidean, but then so is any smooth coordinate manifold. — Cheers, Steelpillow ( Talk) 11:57, 12 November 2019 (UTC)