Cartesian Coordinates in Linear Algebra and Globality

[Bacle]

Hi, Everyone:

I just read recently a comment to the effect that Descartes never intented
his use of coordinates in his layout of analytic geometry to be used globally;
there was also a follow-up comment about " no one really using any coordinates
in a global way. Does anyone know if this is true either way?


( Maybe this is more of a history of Math question, but let me try it here)

Thanks.

 

[Some Pig]

How about longitude and latitude?

 

[Bacle]

I'm not sure I get your point.

 

[HallsofIvy]

Of course, you cannot use Cartesian Coordinates "on a globe" if it was meant that way!

If you assume a mathematically flat plane, then you can use Cartesian coordinates "globally" but I suspect this is talking about applications to physics in which there is no reason to believe that the universe is "globally" flat.

 

[Some Pig]

Cartesian Coordinates can be in any dimensions.

 

[Bacle]

Yes, I understand most manifolds need more than one chart, but I thought the
comment was related to Descartes' use of coordinates.