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isovolume problem

The isovolume problem askes: What surface encloses the maximum volume per unit surface? The answer is a sphere, for which:

volume/surface area = (4/3πr 3)/(4πr 2) = 1/3r

where r is the sphere's radius. Proof of the solution to the isovolume problem came as recently as 1882 from Schwarz.

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   • isoperimetric equality

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