Given a fixed volume of a solid, what would be the shape of such solid that would minimize the its surface area? How to determine it?
I thought about it, but I cannot find an algorithm that doesn't require trial and error.
2026-03-27 23:22:19.1774653739
Highest Volume/Area Ratio
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It's a sphere, because balloons are spherical, and they will assume the shape of minimum area because that also minimizes the strain energy in the rubber.
Some people object to "proof by pictures", and I don't suppose they'd like this "proof by bubbles and balloons", either. But you didn't ask for a proof, and only you can decide if the bubbles/balloons argument is convincing for you. If you really want a rigorous mathematical proof, I expect it's going to be complicated, because the 2D version (with circles) is already quite difficult to prove rigorously. As the comment said, researching "isoperimetric property" will get you started.