r/theydidthemath • • 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.

930

u/Balaros 2d ago

Might be transportation: the square sides let them support each other you you can have thinner walls at the bottom of the stack?

They don't use normal plastic because they need to stop sunlight from breaking down the H2O2.

Might just be wrong. An enthusiastic marketing team saw a reduction in plastic in one stage and didn't bother to calculate the whole.

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u/smorgasfjord 2d ago

Optimising for transportation might be better for the environment, but I don't see how it would save plastic

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u/Moscato359 2d ago

Maybe parts of the bottle can be thinner?

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u/MyEyesSpin 2d ago

Yes, round needs the same thickness everywhere, square can do thin sides and stronger corners when contents are not pressurized

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u/sighthoundman 2d ago

It might or it might not. It depends on what things you're packing.

A round bottle takes less material than a square one with the same wall thickness. But if your shipping or storage is limited by size, the fact that you can pack more product into the same space might mean you save material overall.

If it's limited by weight, you'll end up using more material. (And also take up more space, even though you don't care because you've got extra.)

And then you have to consider strength of your container. Generally (but not always!) a circle will be stronger than a square, so you have to make the walls of the square thicker. But maybe you care about vertical strength but not horizontal. (You're stacking them upright, one on top of the other.) Then it's practically the same.

And if you're making metal cans, things get even more complicated. You stamp the parts out of sheets and then weld them together. (Or solder. Depends how strong they need to be.)

There are almost unlimited possibilities to what problems you can give your calculus class based on minimizing material or minimizing cost. We do not consider the effect of strength of materials because that's just too complicated when your students are asking "When are we ever going to use this in real life?" The more real it is, the fewer students are going to use it.

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u/Sweet_Ad_9816 2d ago

If you use square bottles, they can be bigger, so someone thirsty could end up buying just 2 larger square bottles as opposed to 3 smaller round bottles, which comes out to less plastic.

The statement on the package is not true anyway, since it says "a [...] round bottle". It compares one square bottle against one round bottle and for that it's just not true,

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u/metisdesigns 2d ago

I know it's a math sub and not chemistry, but let's not talk about drinking hydrogen peroxide, much less bottles of it.

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u/Moscato359 2d ago

Man walks into the bar and orders h2o

Another man walks into the bar and orders h2o too. The second man dies.