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Beautiful Symmetry

It has been a very difficult time of late. The sudden unexpected passing of the person who has had the most significant developmental influence on my life continues to cast a long shadow over my life (as it should). My thoughts and focus has been poor. I still learn a lot and derive a lot of satisfaction from Mathematica Stackexchange.

This post is to share a beautiful answer by user ybeltukov that converts the problem to a simpler spherical one and exploits the symmetry.  The answer is here (beautiful).

ellipsoid

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