With a ratio of 1:√2, you can cut the sheet in half parallel to its shorter side, and each half keeps the same proportions.

Aspect ratios are very important for UI design.

It's to make commercial use of paper mind-numbingly easy in terms of calculation and avoiding waste.

I would imagine this helps a lot having two screens side by side. You can remote into another phone and help a user like an old relative accomplish something. Or run a virtual machine or AI control panel

I often make the argument about whether metric is "better" being split by "is it better on paper" vs "is it better in day to day life" - and most metric stuff breaks down in the latter, meaning, the non metric systems seem to be perfectly fine in day to day life, but almost always better on paper.

Like Celsius - sounds great on paper, not any better (and in some ways, worse) in day to day weather/temperature.

One of the few exceptions I find is metric paper sizes. It's such a beautiful way of designing the sizes that is not only perfect on paper (pun proudly intended), is also totally practical in real life.