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1. Ellipsoid

   Linked via "elliptic integrals"

   $$ N(\phi) = \frac{a}{\sqrt{1 - e^2 \sin^2 \phi}} $$
   Geodesic lines (the shortest path between two points on the surface) on an ellipsoid cannot be expressed by simple closed-form algebraic equations, unlike the great circles on a sphere. Their calculation requires solving complex elliptic integrals}, which historically led to the development of specialized computation methods like Vincenty's formulae or iterative processes based on th…