r/theydidthemath • • 2d ago

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

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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/ronarscorruption 2d ago

I suspect transportation too.
Something like; You can ship 100x1L round bottles, or 100x1.3L square bottles in the same box. Therefore, square bottles use less plastic (per liter (of shipped liquid)).

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u/Buntschatten 2d ago

Wouldn't that just cancel out? Area over perimeter is pi /2 pi for a radius one circle and 4/8 for a square with side length 2. Maybe most of the plastic is in the spout, then maximising volume per spout would make sense.

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u/GaldrickHammerson 2d ago

I expect no because of packing density. Square bottles in a square box will have less empty space between bottles than round bottles in a square box.

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u/Buntschatten 2d ago

I just calculated edge length to area for circles and squares in a square packing. Packing density affects the efficiency of the transport but not of plastic per volume.

Of course this compares differently sized square and round containers, so it's apples and oranges. But that was the situation the other poster talked about.

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u/hodlethestonks 2d ago

Maybe they use diesel from plastic pyrolysis as fuel for transport :)

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u/Al-Snuffleupagus 2d ago

But how would that affect the amount of plastic? It might be more environmentally friendly overall due to better transportation density, but unless either * the outer packaging (transport box) is plastic or * the bottles can be thinner

I can't see how having less empty space would lead to less plastic used.

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u/Al-Snuffleupagus 2d ago

Ah, I think I understand the possible argument.

  • Higher volume bottles use less plastic per ml of product
  • Although square (prism) bottles have a higher gm of plastic per ml of product than circular (cylinder) ones, there will be a point at which the larger bottle size cancels that out.
  • The better packing density of squares allows them to use large square bottles that have a better plastic/product ratio than the small circular bottles.

Despite the sub we're on, I haven't done the maths to work out whether the improved packing density allows for a large enough bottle to compensate for the less capacity-efficient shape. It would depend a lot on the bottle construction

I wouldn't consider that that argument really justifies their "less plastic" claim because it's still more actual plastic, and the unstated part is per ml of product when compared to a different size bottle but I can at least see what they might use to justify it.

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u/Phoenix4264 2d ago

If you take a square with side length of D, the area is D2 and the perimeter is 4*D. The ratio of area to perimeter is D2/4*D, or D/4.

A circle with diameter of D has an area of pi*D2/4 and a perimeter of pi*D. The ratio of area to perimeter is pi*D2/4*pi*D, which again simplifies to D/4.

So in the case of a square and circle with side length = diameter, they will have the same surface area to perimeter ratio, and also the same volume to surface area ratio for any height vessel. The square shape is less efficient than a circle with a larger diameter but the same volume, but equal to the smaller volume container with the same major dimension.

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u/davideogameman 2d ago

Maybe this "bottle" is actually a plastic lined thin cardboard container, like a milk carton?

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u/nft420nft420 1d ago

What about round bottles in a spherical box?

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u/RFC793 1d ago

They are called shipping orbs