Geometry Looking for books (or papers) on the Cartesian coordinate system

[Trysse]

I am looking for more books like this one: https://archive.org/details/MethodOfCoordinateslittleMathematicsLibrary
Method of Coordinaes (Little Mathematics Library) by A. S. Smogorzhevsky

I am also interested in papers if you can suggest any. I am interested in texts, that explore the idea of coordinate systems. Suggestions on texts that explore historical developments are also welcome.

 

[mathwonk]

I would suggest first that you actually read thoroughly the book you have found. If you have done that you might google search on cartesian coordinate systems, even read the original work by descartes on geometry. when i googled i found an interesting little article you may like on a few special types of different coordinate systems, cartesian, curvilinear, polar, and homogeneous. you may like it:

https://codinghero.ai/8-different-types-of-coordinate-systems-explained-to-kids/

This is more advanced, but as you may know there are many different plane "geometries", some capable of having Cartesian coordinates introduced and some not, depending upon which axioms they satisfy. This question is extensively studied in Hartshorne's Geometry: Euclid and Beyond, basing on the original research of Hilbert in his Foundations of Geometry. The topic is treated, following up on the earlier fundamental material, in chapter 4 of Hartshorne: "Segment arithmetic". Briefly, to have Cartesian coordinates, the geometry needs the parallel postulate.

 

[Muu9]

Method of Coordinates by Gelfand