Definition talk:Coordinate System/Coordinate

The context into which to place the definition of "coordinate" is wide open. --prime mover 12:51, 7 May 2011 (CDT)

Ah, I searched for it with a hypen, so didn't see there was a page. Perhaps "Coordinate (Manifold)" / "Coordinate (Geometry)" and a disambiguation page? They're kind of the same and kind of different, so I'm not sure --Linus44 13:12, 7 May 2011 (CDT)


 * Actually there's three ways of doing it:
 * a) All on the same page with some weasel-words as to how they're sort-of the same sort of concept a-bit-ish.
 * b) Two separate pages with a disambiguation page, and a separate page demonstrating how one is isomorphic (in whatever sort of categorical context), sort of what we have now.
 * c) One main page with the two separate pages describing the two entities included (with appropriate onlyinclude sections) as transclusions.
 * My vote would be for c), as the concepts are too close to be disambiguated as separate definitions, but too different to go on the same page. --prime mover 14:19, 7 May 2011 (CDT)

Def'n of Origin
The page says:

The origin of a coordinate system is the zero vector.

Now, correct me if I'm wrong, but aren't the zero vector and the origin different things?


 * $O = (0,0,\cdots,0)$


 * $\mathbf{0} =$ the vector with initial point $O$ and terminal point $O$? --GFauxPas 19:31, 25 January 2012 (EST)


 * You may have trouble thinking of vectors as other things than well, arrows with tails and heads. The meaning of zero vector in this context is simply what is on the definition page: the identity under addition. By abuse of language, it has been called a vector (because of the bijective correspondence between vectors and their end points). Simply put: I think it is not sensible to talk about a general vector (an 'arrow') in this generality. That must be saved until after an origin has been chosen.
 * That is, the zero vector ('arrow') is not the same as the zero vector. You are allowed to be a little confused. --Lord_Farin 07:49, 26 January 2012 (EST)
 * Oh, okay. Is there a better way to state the concept of the "vector arrow"? Also, to what extent is the distinction between the zero vector and the zero scalar necessary in $\R^1$? --GFauxPas 12:25, 26 January 2012 (EST)
 * I don't know how to state it better; It's been long since I last bothered about 'vector arrows'. I could imagine a definition in ordered pairs (base point, end point) but I'm not sure what is standard here. The zero vector as on PW is identical to the zero scalar in $\R^1$, as the latter is the identity of addition. It is a bit peculiar to talk about $\R$ as a vector space over itself as it is so intuitive. The zero 'vector arrow' would then be the ordered pair of the zero vector and itself in the possible definition just mentioned. --Lord_Farin 12:44, 26 January 2012 (EST)
 * LF you explained that really well. That's what I thought about $\R^1$. Anyway, as your explanation enlightening, I think you should put something about the misconception I had on Definition:Vector, as I think it's a common misconception. --GFauxPas 12:53, 26 January 2012 (EST)

Direction of this page
I'd say that there are three different concepts bearing the name 'coordinate':


 * Coordinate (Set Theory) - an element of a tuple
 * Coordinate System - an ordered basis for a module (instantiates to vector spaces)
 * Local Coordinate - a diffeomorphism to an open in Euclidean space from some locally Euclidean space (currently called a 'coordinate system' as well, really awkward terminology)

These are not really related, so that I suggest they go on separate pages and this becomes a disambig. --Lord_Farin (talk) 15:57, 30 November 2012 (UTC)


 * Hm, just recalled that 'local coordinate' isn't really accurate; it should be chart. I'll change it to that if we pursue atlas in place of Definition:Differentiable Structure (then an atlas consists of charts, which is nice). --Lord_Farin (talk) 16:16, 30 November 2012 (UTC)