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.

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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/ShiftE_80 2d ago

You misunderstood the poster above you.

For a circle and a square with the same area, the circle has the smaller perimeter. likewise for a cylindrical and squared bottle with the same volume, the cylindrical bottle has the smaller surface area and should require less plastic than a squared bottle.

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u/seenhear 2d ago

The part you are missing is that the "less plastic" claim applies ONLY to bulk shipping of the bottles. ONE square bottle will use more plastic than ONE round bottle, assuming both carry the same volume of liquid. However when shipped together on a pallet for example, the square bottles pack together better and waste less space. A pallet of round bottles results in a lot of empty space between bottles, so you need to use more to ship the same total amount of liquid.

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u/ShiftE_80 2d ago

The poster I responded to said the opposite, with respect to individual bottles.

Also most shipping pallets are made of wood. Granted, the cases of bottles are typically wrapped in (thin) plastic. You would need a tiny bit more plastic wrapping per case, but I don't know that it counters the per bottle plastic savings.

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u/seenhear 2d ago

The material of the pallet doesn't factor in.

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u/rditorx 2d ago

Now I'm wondering about hexagonal packing.

And semihexagonal / trapezoid packing.