Cartesian Coordinates in Linear Algebra and Globality

In summary, the conversation discusses whether Descartes intended for his use of coordinates in analytic geometry to be used globally or not. There is a question about whether anyone knows the truth, and a suggestion that this may be more of a history of math question. The conversation also touches on the use of longitude and latitude, the limitations of Cartesian coordinates on a globe, and the possibility of using them in multiple dimensions. It is also mentioned that Descartes' use of coordinates may be related to applications in physics and the concept of a globally flat universe.
  • #1
Bacle
662
1
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.
 
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  • #2
How about longitude and latitude?
 
  • #3
I'm not sure I get your point.
 
  • #4
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.
 
  • #5
Cartesian Coordinates can be in any dimensions.
 
  • #6
Yes, I understand most manifolds need more than one chart, but I thought the
comment was related to Descartes' use of coordinates.
 

What are Cartesian coordinates?

Cartesian coordinates are a mathematical system used to represent points or locations in a two-dimensional or three-dimensional space. They are named after the French mathematician and philosopher, René Descartes, who developed the system in the 17th century.

How are Cartesian coordinates used in linear algebra?

In linear algebra, Cartesian coordinates are used to represent vectors and matrices. They allow us to perform operations such as addition, subtraction, and multiplication on vectors and matrices, making it easier to solve complex equations and systems of equations.

What is the relationship between Cartesian coordinates and globality?

Cartesian coordinates are used to describe the position of objects in a global sense, meaning they are not relative to any specific point or location. This allows for a universal understanding and communication of positions and movements in a given space.

Can Cartesian coordinates be used in higher dimensions?

Yes, Cartesian coordinates can be extended to higher dimensions, such as four-dimensional space or even higher. This is important in fields like physics and computer graphics, where higher dimensions are often used to model complex systems and environments.

Are there any limitations to using Cartesian coordinates?

While Cartesian coordinates are a powerful tool, they do have limitations. They can only be used to represent objects in a Euclidean space, meaning they may not accurately describe curved or non-Euclidean spaces. Additionally, they can become more complex and difficult to visualize in higher dimensions.

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