Making maps "compatible" with each other is one of the tasks of differential geometry. Calculations done on one map may not be usable on another if maps are not compatible. In the map in the center, the
tropic of cancer is a smooth line; in the map on the left, it has a sharp corner. Calculations done for the map on the left cannot be re-used for the map in the center. The center map and that on the right are compatible.