Lambert Azimuthal Equal-Area Projection

In the present study, we give the proofs about important properties of Lambert azimuthal projection, like conformality, preserve area e.g. which characterizes it. While there are some kind of Lambert projection for instance standard, cylindrical in the literature, we utilize from the south polar aspect and in our proofs, we use this approach. Finally, we give some visualizations of the inverse of projection as an example.