I have 2 points $A=(x_A,y_A), B=(x_B,y_B)$ on a unit circle $O$. The distance between $A$ and $B$ goes through the perimeter of the circle. How can I transform this space to a space with higher dimensions where the distances can be computed using Euclidean formula, and the original distances are preserved as much as possible? In fact, I don't know what is the main field of math concerning such transformations.
Your help is appreciated.