Abstract
Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on nding the inverse forms of van der Grinten projections I-IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations.
Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement and are applicable to the coordinate transformations.