Why does a sphere have the lowest surface area out of all 3D shapes for a given volume?
In: Mathematics
The mathematical proofs are definitely not eli5. Here is a different way to think about it.
One could reduce the problem 2D : why does a circle have the least perimeter for the same area?
One could further reduce the problem to 1D: why is the shortest way between two points a straight line? Because every other way involves a detour from the shortest path.
Now generalizing to 2D: a circle is is the shortest way to “sweep” an area, because at every point we are the shortest distance from the center as possible. Every other way involves a detour i.e. the distance from center becomes larger than what is required to sweep the area. If this distance from the center becomes larger, then we are increasing the perimeter.
In the same way, we can generalize to a sphere in 3D.
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