Talk:3-sphere
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I don't understand how the geometric definition differs from the topological one. In fact, the geometric one appears wrong without further explanation. The 3-sphere is normally taken to lie in 4-space, not 3-space, at least, it cannot be embedded in any way in 3-space. Also, how does the geometric structure differ from the topological? ("In the sense of Coxeter" doesn't impart much...are you considering it as a smooth manifold, or Reimannian manifold, or what? What does "geometric structure" mean here?) Revolver 23:21, 11 Jul 2004 (UTC)
I believe he just means what we would call a 2-sphere. It would appear that some people (Coxeter?) use a different notation though I've never come across it personally. I'm thinking about reverting this to how it was. We can add a sentence remarking on different conventions. -- Fropuff 00:14, 2004 Jul 12 (UTC)
- I suspect that I am the 'he' referred above?
- I disagree with the statement that 'In mathematics, a 3-sphere is...' since this is the topological definition only (with which I am acquainted). Mathematics used to contain both geometry and topology. Geometry uses a different notation - for example, see H. S. M. Coxeter, the 'greatest geometer' of the 20th century - he used 2-sphere for the circle and 3-sphere for the ball. See Eric W. Weisstein. "Hypersphere." From MathWorld--A Wolfram Web Resource. [[1] (http://mathworld.wolfram.com/Hypersphere.html)]. Eric is clear on the distinction between the two terminologies within Mathematics. My edits to this page were intended to make this clear. At the moment, any reader could be forgiven for thinking that Mathematics=Topology and that Geometry doesn't exist. Ian Cairns 00:58, 14 Aug 2004 (UTC)
- You haven't given any reference for this supposed use in geometry other than MathWorld, which is not a reliable source. And the MathWorld article you cite doesn't say that Coxeter used the terms 2-sphere and 3-sphere anyway (it says two-dimensional sphere). So you have provided no meaningful evidence for this unusual use of the term 3-sphere. --Zundark 12:33, 14 Aug 2004 (UTC)
I am a little unsure of where you draw the line between topology and geometry. Most consider one to be a branch of the other. They are certainly intimately intertwined. I have never been aware of a "topological" nomenclature for spheres versus a "geometrical" one. Every mathematician I know—geometer, topologist, or otherwise—uses the definition stated here. However, even accepting that there are other systems in common use, I think Wikipedia should stick to one system for consistency. I think it is enough to leave a note mentioning other usages (which I did). -- Fropuff 02:55, 2004 Aug 14 (UTC)
- I have removed the note, as it does not appear to be true. --Zundark 12:33, 14 Aug 2004 (UTC)
any chance of a picture? -- ssam 21:34, 27 jan 2005 (utc)