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Mollweide map projection and Newton's method
The Mollweide equal-area projection map requires solving a nonlinear equation. Newton's method solves this equation well except at high latitudes.
The lines of latitude are not quite evenly spaced; some distortion is required to achieve equal area. There is no closed-form solution for θ as a function of φ and so the equation must be solved numerically. The reason Newton’s method slows down for high latitudes is that f and its derivative are both at π/2, i.e. f has a double root there.
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