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Ellipsoid surface area calculator: estimate the surface area of an ellipsoid from three semi-axes or three diameters using Thomsen's formula, and reverse the formula to find a missing axis from the area.
$$A\approx 4\pi \left(\frac{a^p b^p+a^p c^p+b^p c^p}{3}\right)^{1/p}$$$$p=1.6075$$
Uses Thomsen's approximation with p = 1.6075.
