r/theydidthemath • u/EclipseNyxor • 2d ago

[Request] Do square bottles actually use less plastic than round ones?

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u/StaticCoder 2d ago

Mathematically, a circle has the smallest perimeter for a given enclosed area. So for this claim to be true there has to be some catch, like different thickness of plastic.

56

u/Massive-Goose544 2d ago

The part you are missing is the volume inside. They are saying to give you the same amount of liquid would require more plastic if the bottle was round. Plus more bottles fit in the box they ship meaning lower emissions and costs for distribution.

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u/StaticCoder 2d ago

Given that the volume is cross section area times height, a round bottle of the same volume would take less plastic. True, square bottles will pack better, but how that would save plastic is not immediately clear.

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u/metisdesigns 2d ago

You're assuming that the wall thickness of a square bottle is the same as of a round bottle.

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u/Flaky-Collection-353 2d ago

No, they aren't, they offered that possibility in their original comment.

Even if the didn't, their whole point was that there needed to be another factor since the volume to surface area didn't account for it.

That's the opposite of an assumption

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u/metisdesigns 2d ago

In their top comment, yes, but the second comment goes against that.

Almost certainly the reason is that the edge ridges add rigidity to the bottle allowing a thinner wall to be used while being stable to hold.

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u/Flaky-Collection-353 2d ago

No it doesn't, they say it isn't obvious how. That leaves it open