I am trying to understand a mathematical idea used in a physics experiment. I am trying to understand conformal mapping in regards to an experiment I did for a physics class. So there was this derivation of a method to measure the resistivity of a conductor done by a person called Van Der Pauw. This method requires conformal mapping though. "He showed that conformal mapping (conformal transformation) can be used to image any singly connected thin sheet of uniformly conducting material with four point contacts on its periphery on a half plane. The contacts will lie on the half plane border."
And then I read about conformal mapping "In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths." What does that mean? How are the angles preserved in this diagram and the lengths changed? It seems to me that the lengths between points like 1 and 4 are probably different, but the angle is changed as well? I've looked at other diagrams of angle preservation and they just show a grid of intersecting lines that maintain intersection at the same angle after transformation. I don't know how to interpret it though.
