Transform Coordinate System: Curvy to Euclidean Space

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Transforming a curvy coordinate system to Euclidean space involves understanding the relationship between the two systems, often using mathematical functions. The discussion clarifies that "curvy" refers to non-Cartesian systems, such as polar coordinates. An example provided illustrates this transformation in a two-dimensional Euclidean plane, demonstrating how to convert polar coordinates to Cartesian coordinates. The key takeaway is that regardless of the coordinate system used, the underlying space remains Euclidean. Understanding these transformations is essential for applications in geometry and physics.
TimeRip496
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How do you transform a curvy coordinate system to that in euclidean space? An example will be greatly appreciated.
 
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TimeRip496 said:
How do you transform a curvy coordinate system to that in euclidean space? An example will be greatly appreciated.

I presume that by "curvy coordinate system" you mean "a coordinate system that is not Cartesian"?

The space is going to be Euclidean or not no matter which coordinates you use; I posted an example for a two-dimensional Euclidean plane in which the "curvy" coordinates are polar coordinates in your other thread.
 

Thread 'Am I understanding the concept of proper frame of reference?'

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