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All this manual calculation rather than just invoking the isoperimetric inequality? I mean, manual calculation isn't bad, if you want to do it also as an addit
by Sniffnoy 1y ago
All this manual calculation rather than just invoking the isoperimetric inequality? I mean, manual calculation isn't bad, if you want to do it also as an additional demonstration, but I think the isoperimetric inequality is worth a mention here!
- dreghgh 1y agoThe calculation is somewhat bogus since comparing a sphere and a torus with the same radius isn't really valid. The author should either compare the surface areas of spheres and toroi with the same volume, or vice versa.
- jrichardshaw 1y agoThe author does indeed do that via their definition of the volume equivalent sphere radius r_s.
- gus_massa 1y agoThe isoperimetric inequality is correct but too short. You need a longer proof with more equations and integrals to convince people.