I have gone through many Wikipedia documents on geometrical spaces such as Euclidean space, and geometrical systems of representing points such as Cartesian.
But the terms used is confusing me. Sometimes the article says Euclidean space, sometimes Euclidean system. So my question is what is the correct way of writing these?
Can someone list the
- different spaces ( Euclidean, Elliptical etc. )
- the geometrical jargon for representing points on these spaces ( Cartesian, polar etc )
- which space fits which which coordinate system?
I am assuming that there might be a space for example Hyperbolic, where you cannot use Cartesian representation.
Concrete examples would be great, for example that the parallel postulate works only with the Euclidean space and not with the Elliptical space. And if possible one intuitive practical application of the usage of the space + system.
The question is quite broad, but I am unable to find a single article where there is a entire summary of all the spaces, systems and their applications.