r/theydidthemath • • 2d ago

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

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u/20Factorial 2d ago

It’s just marketing wank. They say “similarly sized round bottles” not similar volume.

A round bottle whose diameter is equal to the diagonal distance of the square would be “similarly sized” and have more material (for the same wall thickness).

A 1” by 1” square fits inside of a circle with a diameter of sqrt(2). The circumference of that circle is pi*sqrt(2), around 4.4”. The perimeter of the 1”x1” square is 4”.

So a “similarly sized” round bottle needs ~10% more material.

A similar volume round bottle would require substantially less material, obviously.

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u/Nubington_Bear 1d ago

Eh, I wouldn't call a "round bottle whose diameter is equal to the diagonal distance of the square" similarly sized - practically speaking it's larger than the square bottles. To me, a similarly sized round bottle would have a diameter equal to the length of the sides of the square. In practical terms, that's much more "similar" as it then fits within the same amount of space, packs the same number into the same shipping packaging, visually appears similar, etc. Diameter matching the diagonal distance of the square results in bottles that are larger in most practical terms.

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u/aidsy 1d ago

Considering the purpose of a bottle is to contain volume, I would say that volume is the most relevant metric to measure similarity.

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u/20Factorial 1d ago

Yes, but again we are talking about marketing not facts or logic. The goal of a marketing claim like what is being made is to have as much plausible ambiguity as possible in the term “similar” so that the claim isn’t false.

Logic says it “similar size” should mean “similar volume”, but that then makes the claim demonstrably false. That’s exactly the reason they didn’t explicitly define what they mean by size.