to be projected. The map has area 4R, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R, 2R], and the y-coordinate has a range of [−R, R]. Equation (1) may be solved with rapid convergence (but slow near the poles) using Newton–Raphson iteration: If φ = ±, then also θ = ±. In that case the iteration should be bypassed; otherwise, division by zero may result. There exists a closed-form inverse transformation: where θ can be found by the relation The inverse transformations allow one to find the latitude and longitude corresponding to the map coordinates x and y. See also List of map projections Aitoff projection Hammer projection Tobler hyperelliptical projection family Notes References External links An interactive Java applet to study deformations (area, distance and angle) of the Mollweide Map Projection Mollweide Projection at Mathworld Map projections Equal-area projections