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It (A4) has tolerances of 2mm on either side though so you can go as close to a √2 ratio as you want :) Not sure about the tolerances on letter paper.

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The fact is has loose tolerances seems a bit non-sequitur, but thanks for sharing. In both cases, I was using the “standard” dimensions.

Loose is relative. I suspect a 2mm tolerance in office paper wasn't considered loose in 1921.

Is there a point you are trying to make? A4 is by definition the size I stated in my comment. The square root of 2 isn’t some universal “perfect size” around the globe for paper. Those who use A* might prefer it, but there is a lot of variation across the globe on what defines “paper” size as “normal”. There’s also folks who use the B* series of sizes for example.

The definition of A4 includes the tolerances. And the only reason it doesn't perfectly match the square root of two is rounding. It's not a non-sequitur to point out that 1/√2 is at the core of A4, not the particular millimeters you quoted.

Neither tsbinz nor sjwright was saying anything about whether 1/√2 is a "perfect size" or not.

The B* series is also 1/√2.

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