Talk:Möbius strip/Archive 1

message: After sifting through the above discussion and a lot of tinkering around, I have stumbled upon a very nice desription of the Möbius strip with a circular boundary.
The first step is to embed the Möbius strip in the 3-sphere (thought of as a subset of C2) via the maps
:z_1 = \sin\eta\,e^{i\phi}
:z_2 = \cos\eta\,e^{i\phi/2}
Here η runs from 0 to π and φ runs from 0 to 2π. The boundary of the strip is given by |z_2| = 1, which is clearly a circle on the 3-sphere.
The second step is to map S3 to R3 via a stereographic projection. Stereographic projections map circles to circles and will preserve the circular boundary of the strip. In order to get a finite surface one must project from a point not on embedded Möbius strip in S3. After some trial and error I found that projecting from the point (½,−½,−½,−½) looks quite nice. The resulting surface looks similiar to the one shown above. (I can upload Mathematica graphics if anyone is interested).
:Absolutely, I'd love to see it!  Your description is a lot cleaner.  (I guess it has fewer knobs for sculpting the surface, but that's a good thing.  More natural, less hacky.  I can't visualize 4D projection in my head (yet!), but the Möbius-Strip-In-4D with which you're starting has an awesome symmetry to it.)  -- Anonymous Reader.  8:35, 29 September 2005 (UTC)
thread_title: A nice description

message: It would certainly make for easier editing. Klosterdev 20:29, 6 March 2006 (UTC)
replies: text: If you can't type an "ö" easily, you could always just write "Mobius" and let someone with an "ö" key fix it.  The regexp replace user script makes fixing such things particularly easy.  —Ilmari Karonen (talk) 21:07, 6 March 2006 (UTC)
replies: text: There is an entirely standard way to represent a German o-umlaut when you don't have an umlaut symbol: you just put an e after the o. So among mathematicians, at least, an entirely standard alternative to "Möbius" is "Moebius". (But definitely *not* "Mobius".)Daqu 19:27, 7 August 2006 (UTC)
thread_title:  Should we replce Möbius with Mobius? 

message: The strip is the symbol of the Humanist International and also of many humanist parties (ex: Portuguese Humanist Party  ). I think that should be refered in the article. Mário 00:05, 23 March 2006 (UTC)
thread_title: Humanist symbol

message: Hi to the contributors - great work. I'd love to nominate this as a Good Article but I fear it would be shot down by reviewers for a lack of references. Anyone think they could add a few? Inline citations would be great too - no harm in asking eh? Cheers SeanMack 16:37, 11 April 2006 (UTC)
replies: text: Searching the net I came across chemistry papers talking about aromatic compounds with Möbius strip shapes, for example here, 
http://www.rsc.org/ej/CC/2000/b002462g.PDF, any chemists know enough about this to do it justice? SeanMack 18:10, 30 May 2006 (UTC)
thread_title: Good Article, but...

message: in the topology subsection the first paragraph talks about a diagram on the left which is nowhere to be found (at least on mobile version) Alexthunder27 (talk) 16:07, 3 March 2020 (UTC)
replies: text: I moved the image.  It should be visible in that section now. — Anita5192 (talk) 16:53, 3 March 2020 (UTC)
replies: text: We should not be talking about positions of images at all. They are usually different for mobile viewers than for viewers on large screens. See MOS:SEEIMAGE. —David Eppstein (talk) 18:32, 3 March 2020 (UTC)
thread_title:  diagram missing