After reading Maximilian M. Answer here: Gauss' Theorem - Can't understand a parameterization
I'm trying to figure out why does a figure look the same in every coordinate system I choose.
For example, if I take the unit ball in $\mathbb{R}^2$ , then in polar coordinates, I'll get a rectangle. But, when looking at the figure:
and plotting it in Matlab in Cartesian coordinates, I get exactly the same 3 dimensional figure (and according to Maximilian M., who answered my question, it will be like that for every figure I choose. I tried replying over there, but he probably missed this question of mine).
So:
For a three dimensional figure given in a specific coordinate system, do we get exactly the same figure after moving to another coordinate system?
Hope you will be able to help me understand it geometrically and understand what am I getting wrong here.
Thanks in advance !