This video nicely explains the benefits of A4 paper and may also trigger an existential crisis:
Fountain Pens
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Can't explore the scales of the Universe quite as easily with letter paper!
Is it just the size difference or is the ratio also different? I am too tired to grab my calculator.
It's the same, the difference is the starting "0" size. For the A-series, the area is 1 m^2. For the B-series, the shorter side length is 1 m. The C-series is the geometric mean of the areas of the A- and B-series.
It's sqrt(2) for all formats. As you may know, that means you can fold it in half and still have an aspect ratio of sqrt(2).
When I was a student, all my notebooks were either A4 or B5, these days even A5 is too big for me and I end up with A6 for most of my handwriting stuff.
Never seen a C-series paper though, didn't even know it existed.